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Bro if I really get my degree it is solely due to this man. Like seriously, everytime I look up a topic he has it and does it perfectly. Im gonna drop $30k on his Patreon
Hey there! Again many thanks. You need to a page where we can donate for your videos. You are just that good! I would totally donate $ for all the ways you have helped me!
I was about to drop Calculus AB since I found it so difficult. However, I found your channel and you got me through Calculus AB, BC, Chemistry, Physics, and finally Differential Equations and classes I was once struggling in became far more manageable. You saved my grades and my mental health and I was able to get into my dream school of JHU for mechanical engineering thanks to you. Thank you so much for all you have done for me and other students like me.
Love how you teach, it's really amazing..you got amazing tricks to which enables us to grasp content ..I think most students in Engineering Kenyatta University - Kenya love your channel,, your voice as well
Thank you so much for helping me all the way from trigonometry to calc 1-3, chemistry, physics, and differential equations. You're truly an angel. Anyways can you please make merch that actually says "The Organic Chemistry Tutor"?!
I am really confuse where should you place the "c" because it does matter on where you would place the c because you will get a completely difference answer. Lets take for example on you last example. The general solution I got was: lnx^2 = e^(y/x) +c Now when I computed the value of c, I got 0 = 1 +c c = -1 Instead of e^(y/x) = lnx^2 +c 1 = 0 + c c = 1 Please do clarify on this one because I am having confusions. Thanks!
Keep making differential equations videos the whole book lectures if possible. I have been able to learn solid calculus 1 and 2 because of you it would be highly appreciated.
The guy is a blessing, I even study even when I'm on holiday coz he made everything easy to me. He is one of the best communicators and professors I have ever had. He is more than best❤
nature isnt so easy that we can describe its processes easily. Take it from a Physics major, differential equations help us model nature very well..and the more complex system we describe, the more sophisticated do our equations become
Can you explain why we stop at abs(x) = c(x-y)^2? Why is that the desired form? Does it just happen to coincide with applications in the sciences and therefore this is useful for university students?
Great work but you can also write e^c as k, because e^ to a constant maybe a constant, but it's not the same constant "c". It's different so you have to call it something different.
Thats just the special v-subsitution you need to memorize for homogenous equations. You want to see if the function can be a function of y over x. v=y/x is the same as y=vx
Win Ner the goal is to substitute v into the equation so you can turn it into a separable equation in terms of x and v and solve it like that. Then you just substitute your v=y/x back into the equation for the answer
hello! thank you for your great videos! 9:37 why there is lxl? can't we just write x instead of lxl? + I am not sure where do I have to stop changing the equations. any tips for that plz?
See the x on the right side of the equation. The x in C(x-y)^2. Imagine the value of that x is a negative number. Let's say -1. And the value of y is any number. Let's say -4. So C(x-y)^2 is now equal to C(-1-4)^2 = C(-5)^2 = 25C. The point is, no matter the value of x and y is, when you square their difference the value is always positive. Since the value of C is not yet known, it is always implied as positive. So regardless, the value of the x on the left side of the equation must always be positive. That's why it is written as |x|.
My solution: 2xdy= (x+y)dx --> dy/dx = (x+y)/(2x) = 1/2 + y/(2x) Let v = y/x --> y = x * v --> dy/dx = v + x * dv/dx (product rule) Now we know: 1. dy/dx = 1/2 + 1/2 * v 2. dy/dx = v + x*dv/dx --> 1/2-v/2=x*dv/dx --> int(1/x) dx = int(2(1-v)) dv, (int = integral) By using algebra we therefore get: y = x + c*sqrt(x) (we might as well let c be positive because it's arbitrary anyway, for now) Initial condition: y(1) = 0 y(1) = 1 + c = 0 --> c = -1 Hence: y(x) = x - sqrt(x)
Due to COVID-19 Situation , My classes covert from physical to online. A Teacher who even cannot teach Physically good how I can suppose that he can teach brilliantly to use in Online Situation . I literally learn nothing from my teacher however *The organic Chemistry Tutor* become my last hope through which i learn a lot. Thanks a lot buddy you are a lifesaver for me.
Please explain the proper positioning of C. Because, I got lnY + C in the second problem and that would be a problem. I cant transfer it to the other side cause it would be a negative which will not allow the exponent rule of when exponents are added, the variables are multiplied. Its confusing, from the beginning. Again in the second problem, why is that XY dx is in the left side?
You can transfer the C to the other side and still have the positive sign. Since C is an arbitrary constant, the negative of C can still be treated as positive of C
Hello sir , i want to thank you for your helpful videos on chemistry , physics and maths. I think you made a mistake in the video at 6.00 ... c isnt equal to lnc but to lne^c. Then you can continue the same 😁
Professor Organic Chemistry Tutor, thank you for a powerful analysis on First Order Homogeneous Differential Equations. This is where Techniques of Integration in Calculus Two is used for finding solutions to Ordinary Differential Equations. Differential Equations is an extension of Calculus. This is an error free video/lecture on RUclips TV with the Organic Chemistry Tutor.
I was shocked when i heard your voice, because i didnt look at the name of the uploader page and i ve watched your chemistry videos before. You re good man :)
But you don't get it. Differential equations are not solved with a number. They are solved with an actual equation! At school, they gave you "x + 2 = 4", then asked, "what is x?" Now, they give you "dy/dx = 4", and ask, "what equation, when you differentiate both sides, you get dy/dx = 4?". The answer (in this case) is y = 4x y = 4x is the "solution". Differentiate both sides you see. Easy you say? (Don't forget the integration Constant in our solution, also 😉). This time, you just had to integrate both sides, but sometimes you Can't integrate both sides-x and y are simply not separable. Therefore you have to look for other methods. THAT is what studying Differential Equations is all about! Hope makes sense!
Thanks youuu!! Your videos are always so helpful. You are the reason why I am able to understand Organic chemistry and now you are also helping me in Maths. Thanks a lot buddy. 🙂🙂
Accelerated 8wk summer 2023 DiffyQ gang, wya? I know y'all are out here lol You're gonna do GREAT!! You will PASS!! Always go for the A, but ALSO remember: Cs get degrees ;)
For the last question when we get to: e^(y/x) = 2ln(x) -2C Can we not do: e^(y/x) = ln( x^2 ) -2C , sub in (1,0) e^(0/1) = ln( (1)^2 ) -2C e^(0) = ln(1) -2C 1 = 0 -2C C = -1/2 so, e^(y/x) = ln( x^2 ) - 1/2 instead of simplifying e^(y/x) = 2ln(x) -2C into: e^(y/x) = ln( x^2 ) + C , sub in (1,0) e^(0/1) = ln( (1)^2 ) + C e^(0) = ln(1) + C 1 = 0 + C C = 1 therefore(as shown in video), e^(y/x) = ln( x^2 ) + 1 and why?
Why did you put a "1" next to the terms in the numerator at 10:05? You confused the hell out of me for like 15 minutes because I thought they were derivatives. If we are this far into mathematics, I don't think you need to signal that a term is the the "1st" power when we are dealing with diff eq. It just makes it confusing.
I owe you my A grade. Its all thanks to you for real ❤. Then I noticed you dont have a video on Partial differential equations... Please could you make one? A lot of people will benefit for sure..
The idea is that x/x is the same as 1, therefore, there is no need to multiply the right side by 1 again. It will yield the same answer. He just did that to uncomplicate the left side.
Wait, what? e^{y/x} is doesn't matter, and doesn't need to be counted? That's just lucky to having y/x in the exponent, if it was something else, for example, x^2 y, or something else, which in substitution as "y = vx" does not cancelling x, next equation will not be separable/homogeneous. It matter, it's the main thing in homogeneous equations, which can be substitute with something like "y = u * x^k". Since 2 years after publication, I'm watching it. idk why.
instead of this why not rearrange the equation such that wherever you get y/x replace with v and wherever you see dy/dx, replace with v+xdv/dx and move all the same terms to the other opposite sides, integrate and make Y the subject of formula, if possible.
Something I don't understand, isnt the whole point of differential equations is to make y the subject of the equation? for some reason you don't always do that?
Thank you times a thousand man the three examples are up to the point and the explanations are clear and precise. Now i know how to solve homogeneous differential equations.
hi ... i think there is error somehow with general solution for Q1... i used to methods both by integrating factor and by change in variables and i am getting same general solution, that is, y = x + c{x^(1/2)}... please correct me if im wrong guys
Final Exams and Video Playlists: www.video-tutor.net/
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Ok this guy has helped me since trigonometry. Once I make it as a Civil Engineer, I will drop a $1k donation to your Patreon. BET.
Lol, fellow Civil Engineering student here.
Same and right before prelims too
Same bro
imma make sure this man dont gotta work another day in his life.
Bro if I really get my degree it is solely due to this man. Like seriously, everytime I look up a topic he has it and does it perfectly. Im gonna drop $30k on his Patreon
It's safe to say we all owe our degrees to this man here. Thanks a million!
Hey there! Again many thanks. You need to a page where we can donate for your videos. You are just that good! I would totally donate $ for all the ways you have helped me!
www.patreon.com/MathScienceTutor its in the description
I just realized you don't have a video on exact differential equations!
Kindly make one. Others might benefit in the years to come.
Thank you.
Agree
Here's a summary of first order homogeneous differential equation.
10% calculus
990% algebra
Right, that's about FOHDE
100000000% brain
you could never be more right
1110 % true
I was about to drop Calculus AB since I found it so difficult. However, I found your channel and you got me through Calculus AB, BC, Chemistry, Physics, and finally Differential Equations and classes I was once struggling in became far more manageable. You saved my grades and my mental health and I was able to get into my dream school of JHU for mechanical engineering thanks to you. Thank you so much for all you have done for me and other students like me.
congrats on making it to JHU!
Thank you so much!
My son got in but didn't go because he said it would be too much of a grind. How's it going?
Please I need a full playlist of differential equation tutorials.
x2
Go to khan academy
Love how you teach, it's really amazing..you got amazing tricks to which enables us to grasp content ..I think most students in Engineering Kenyatta University - Kenya love your channel,, your voice as well
accurate
My "professor" tried to teach us this in two minutes by doing one problem and moving on to the next section.
Same case my professor just gave a example and moves to bernoulis equations...thanks to this man.
dude mine too. we literally did one example and he was like " aaaalright gl with your homework. and this is gonna be on quiz tomorrow"
My professor tell us to "read" about this.
@@mrx57503:52 3:52
This man has helped me in so many ways. Absolutely grateful.
This gave me anxiety.
You did great, but this is tedious lmao
youre right
Can anyone explain y= dy/dx?
Organic Chemistry tutor is the OG, better explained videos than most of my university classes on basically every subject
I almost never comment, but I thought it was worth it to thank you, now i dont think I'll fail my exam!
Thank you so much for helping me all the way from trigonometry to calc 1-3, chemistry, physics, and differential equations. You're truly an angel. Anyways can you please make merch that actually says "The Organic Chemistry Tutor"?!
I am really confuse where should you place the "c" because it does matter on where you would place the c because you will get a completely difference answer. Lets take for example on you last example. The general solution I got was:
lnx^2 = e^(y/x) +c
Now when I computed the value of c, I got
0 = 1 +c
c = -1
Instead of
e^(y/x) = lnx^2 +c
1 = 0 + c
c = 1
Please do clarify on this one because I am having confusions. Thanks!
The equations must have same dimensions for them to be homogeneous. Great work. Thanks.
Keep making differential equations videos the whole book lectures if possible. I have been able to learn solid calculus 1 and 2 because of you it would be highly appreciated.
Have you graduated whats going on now?
i have the same question lol@@arsh1357
Question, at 2:14 when dividing both sides by x, why is 2x(xdv+vdx) simplified to 2(xdv+vdx) instead of x(xdv+vdx)?
Left side is constant, he only took out the x from the right side as a co_ factor and replace it with 1
the x's cancel so ur left with 2. see: (2x)/(x) = 2
can someone please explain the first example isn't that a linear first order equation , so can we use the integration factor method?
Am a bsc physics student
Whenever I feel I need to brush up my basic knowledge I come here
This guy has helped me more than anyone
Thank you dude
This gives me depression😭
Great video.
All time when I fall in pressure,your video help me,sir.
Thank you very much for your video.
Once I get my degree and a job I’ll donate whatever extra income I get to this guy
The guy is a blessing, I even study even when I'm on holiday coz he made everything easy to me. He is one of the best communicators and professors I have ever had. He is more than best❤
folks need to be careful at 5:34. The -1 is to be considered inside the LN(), e.g., ------> ln [ ( 1 - v )^(-1) ]
Yes. This threw me off
You are one of the reasons I survived first year of engineering. Thanks man !
Why do I even pay tuition when I have access to this?
fr tho
Isn't maths supposed to make solving real life problems simpler?? If so why do we have to go through so much more complications? Just asking
nature isnt so easy that we can describe its processes easily. Take it from a Physics major, differential equations help us model nature very well..and the more complex system we describe, the more sophisticated do our equations become
Thank you bro. Six years later this video is keeping on teaching and supporting math students😊
Can you explain why we stop at abs(x) = c(x-y)^2?
Why is that the desired form? Does it just happen to coincide with applications in the sciences and therefore this is useful for university students?
Great work but you can also write e^c as k, because e^ to a constant maybe a constant, but it's not the same constant "c". It's different so you have to call it something different.
0:44
How do you come up with this equation? y = vx
Why not, y = x + 1
or anything else?
Thats just the special v-subsitution you need to memorize for homogenous equations. You want to see if the function can be a function of y over x. v=y/x is the same as y=vx
@@eashanmathur2030 ok, thank you
Just think of "v" as a variable that allows x to always have the same value as y for all values of y.
Win Ner the goal is to substitute v into the equation so you can turn it into a separable equation in terms of x and v and solve it like that. Then you just substitute your v=y/x back into the equation for the answer
+The Organic Chemistry Tutor
Hello sir , are you going to upload a video in regards to solving second order differential equations?
the second example was a second order DE
All the way from Kenya thanks for making my school life easier .More power to you
hello! thank you for your great videos!
9:37
why there is lxl? can't we just write x instead of lxl?
+ I am not sure where do I have to stop changing the equations. any tips for that plz?
See the x on the right side of the equation. The x in C(x-y)^2. Imagine the value of that x is a negative number. Let's say -1. And the value of y is any number. Let's say -4. So C(x-y)^2 is now equal to C(-1-4)^2 = C(-5)^2 = 25C. The point is, no matter the value of x and y is, when you square their difference the value is always positive. Since the value of C is not yet known, it is always implied as positive. So regardless, the value of the x on the left side of the equation must always be positive. That's why it is written as |x|.
@@ichantongohan5951 i still dont get it :(
My solution:
2xdy= (x+y)dx --> dy/dx = (x+y)/(2x) = 1/2 + y/(2x)
Let v = y/x --> y = x * v --> dy/dx = v + x * dv/dx (product rule)
Now we know:
1. dy/dx = 1/2 + 1/2 * v
2. dy/dx = v + x*dv/dx
--> 1/2-v/2=x*dv/dx
--> int(1/x) dx = int(2(1-v)) dv, (int = integral)
By using algebra we therefore get:
y = x + c*sqrt(x) (we might as well let c be positive because it's arbitrary anyway, for now)
Initial condition: y(1) = 0
y(1) = 1 + c = 0 --> c = -1
Hence: y(x) = x - sqrt(x)
Due to COVID-19 Situation , My classes covert from physical to online. A Teacher who even cannot teach Physically good how I can suppose that he can teach brilliantly to use in Online Situation . I literally learn nothing from my teacher however *The organic Chemistry Tutor* become my last hope through which i learn a lot. Thanks a lot buddy you are a lifesaver for me.
Sir,love your lecture so much..💖💖💖
Thanks & respect from the deepest core of my heart..
Please explain the proper positioning of C. Because, I got lnY + C in the second problem and that would be a problem. I cant transfer it to the other side cause it would be a negative which will not allow the exponent rule of when exponents are added, the variables are multiplied. Its confusing, from the beginning. Again in the second problem, why is that XY dx is in the left side?
You can transfer the C to the other side and still have the positive sign. Since C is an arbitrary constant, the negative of C can still be treated as positive of C
if i pass my DE course in electrical eng, and hopefully go on to become an engineer, i will drop a hefty donation to this guy! helped me alot
did you pass the course?
I WILL BE AN ENGINEER🤞👊🙏
Hello sir , i want to thank you for your helpful videos on chemistry , physics and maths. I think you made a mistake in the video at 6.00 ... c isnt equal to lnc but to lne^c. Then you can continue the same 😁
nope
this is a year late but since lnc can be a value for any constant, it is the same as replacing c (which is a variable representing a constant).
my life line my pookie my everything thank u man
Professor Organic Chemistry Tutor, thank you for a powerful analysis on First Order Homogeneous Differential Equations. This is where Techniques of Integration in Calculus Two is used for finding solutions to Ordinary Differential Equations. Differential Equations is an extension of Calculus. This is an error free video/lecture on RUclips TV with the Organic Chemistry Tutor.
Good luck my fellow engineering students! You and I will both need it :)
Why does the final answer have an absolute x
I was shocked when i heard your voice, because i didnt look at the name of the uploader page and i ve watched your chemistry videos before. You re good man :)
Hey something simple as (VX)^2 is confusing me.
(VX)VX, i am getting V^2(XV)+(VX)X^2
Anyone to help me understand please.
Wrongly applying product rule. For V2X2, freeze V2, differentiate X2 (= 2X) then freeze X2, differentiate (implicitly) V2 (= 2V dV/dX). Add the results (= 2XV2 + 2VX2 dV/dX)
The best mathematics lectures on You Tube and online. bravo prof. You are the best 🙌
Been here since jhs ✊🏻🖤 and now I’m surviving college, thanks alot sir!
9:40
|x|=.....
19:36
y=....
What is actually looked for in the solutions?!
I'm really confused
i went to comments just to find this... i'm so angry rn. it confused me so much.
c square comes to c?
But you don't get it. Differential equations are not solved with a number. They are solved with an actual equation!
At school, they gave you "x + 2 = 4", then asked, "what is x?"
Now, they give you "dy/dx = 4", and ask, "what equation, when you differentiate both sides, you get dy/dx = 4?". The answer (in this case) is y = 4x
y = 4x is the "solution". Differentiate both sides you see.
Easy you say? (Don't forget the integration Constant in our solution, also 😉).
This time, you just had to integrate both sides, but sometimes you Can't integrate both sides-x and y are simply not separable. Therefore you have to look for other methods.
THAT is what studying Differential Equations is all about!
Hope makes sense!
Thanks youuu!! Your videos are always so helpful. You are the reason why I am able to understand Organic chemistry and now you are also helping me in Maths. Thanks a lot buddy. 🙂🙂
Is there a video on exact differential equations?
Bro has a patreon for those who are feeling generous
Accelerated 8wk summer 2023 DiffyQ gang, wya? I know y'all are out here lol
You're gonna do GREAT!! You will PASS!! Always go for the A, but ALSO remember: Cs get degrees ;)
bro this guy is always so clutch. Better teacher than my professor with a doctorate
For the last question when we get to:
e^(y/x) = 2ln(x) -2C
Can we not do:
e^(y/x) = ln( x^2 ) -2C , sub in (1,0)
e^(0/1) = ln( (1)^2 ) -2C
e^(0) = ln(1) -2C
1 = 0 -2C
C = -1/2
so, e^(y/x) = ln( x^2 ) - 1/2
instead of simplifying e^(y/x) = 2ln(x) -2C into:
e^(y/x) = ln( x^2 ) + C , sub in (1,0)
e^(0/1) = ln( (1)^2 ) + C
e^(0) = ln(1) + C
1 = 0 + C
C = 1
therefore(as shown in video),
e^(y/x) = ln( x^2 ) + 1
and why?
Why did you put a "1" next to the terms in the numerator at 10:05? You confused the hell out of me for like 15 minutes because I thought they were derivatives. If we are this far into mathematics, I don't think you need to signal that a term is the the "1st" power when we are dealing with diff eq. It just makes it confusing.
I owe you my A grade. Its all thanks to you for real ❤.
Then I noticed you dont have a video on Partial differential equations... Please could you make one? A lot of people will benefit for sure..
Yes 2006 video still helping. If you know you know.
He deserves all the tuition money i give to my uni
Hhmm🤔Thanks, but it's just that this topic seems hard and challenging to me, so i cant even understand what is going on here😃
Major respect......watching this during quarantine and im absolutely enjoying it!
QUARANTINE FREN HAHA
You are the king bro❤️ i always come back to clear concepts from your videos from school to grad. Thanks man❤️
Why are we able to multiply left side by x but not the right hand side at 8:00? Doesn't that change the equation?
The idea is that x/x is the same as 1, therefore, there is no need to multiply the right side by 1 again. It will yield the same answer. He just did that to uncomplicate the left side.
i'm following this
In the second example you accidentally deleted the dy
You deserve accreditation. Your education videos are university level.
I was facing numerous problems in D. Es but this guy made my life simple
Please watch Professor Leonard Differential Equations Playlist. This professor is awesome.
10:47 pro tip: you can also replace x=vy ; dx=vdy+ydv, makes the solution easier and shorter
for me is confusing your take.
Wait, what? e^{y/x} is doesn't matter, and doesn't need to be counted? That's just lucky to having y/x in the exponent, if it was something else, for example, x^2 y, or something else, which in substitution as "y = vx" does not cancelling x, next equation will not be separable/homogeneous. It matter, it's the main thing in homogeneous equations, which can be substitute with something like "y = u * x^k". Since 2 years after publication, I'm watching it. idk why.
I would like to donate to your channel as well. Great work
Good day everyone.
Pls which app is he using to make this video? Anyone to assist?
This is where I attend my maths class, Thank you so much Prof J.G
26:30 Shouldn't we use ln in the last equation and seperate y/x so it stays only y=....?
Just want to say thank you for the explanation and work, you're fast paced yet clear enough to where I can follow along. Keep it up!
Excellent, can i ask about the program of writing used in explanation.
Man is simply good
instead of this why not rearrange the equation such that wherever you get y/x replace with v and wherever you see dy/dx, replace with v+xdv/dx and move all the same terms to the other opposite sides, integrate and make Y the subject of formula, if possible.
I just want to say from the bottom of my heart, I love you and I will always love you.
Something I don't understand, isnt the whole point of differential equations is to make y the subject of the equation? for some reason you don't always do that?
Really the best, I didn’t understand this lesson in Arabic or French but you made it very easy, keep going I depend on you to pass this year 😂 👏🏻
Thanks man I Got my maths marks 1st Sem, 2nd Sem and i have Grade A for both. Thanks again GOD! Love from SL!
bruh ive been going here since like geometry and as i go up in math level it slowly just turned into people talking about engineering lmao
Your talent will remain as rememberance dear Thanks to almighty father n continues increasing your incredible thought 💖🔥
is there a second order linear homogeneous and non-homogeneous differential equation?
Yes, there is 🙂
Thank you times a thousand man the three examples are up to the point and the explanations are clear and precise. Now i know how to solve homogeneous differential equations.
I thought constant C is always on the integral of dx/x but sir wrote it on the integral of C, im confused honestly
Hey guys, can anyone help me with the solution for this: dy/dx = (2x+y)/(3x+2y)
i'm dropping my first pay as a donation as soon as i graduate, you deserve it.
Man! Thank you a lot for your videos. So well explained that you make it easy. Kudos my man ❤️🙏
❤❤❤❤❤very understandable..thank you very much
hi ... i think there is error somehow with general solution for Q1... i used to methods both by integrating factor and by change in variables and i am getting same general solution, that is, y = x + c{x^(1/2)}... please correct me if im wrong guys
can anyone help me how to solve y'=(x+y-2)2 by using this method please..??
Thank you soooo much prov you're amaizing tbh🥰
Studied from this channel in my 10th now I'm back.. Currently doing Btech
Thanks man for making computer engineering manageable for me
For the last qtn, I ended up with C as -1 but when I move C to the other side, I get the exact answer as in the video! So is this still correct?
Can somebody please explain how did we arrive at -1ln[1-v] at the 1st sum?
Siyanda Msimango Integrating factor
@@tarachristinarogge2405 U substitution