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
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.
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❤
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!
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
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.
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.
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"?!
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.
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.
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 :)
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 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!
Ay bro imma drop a mad amount on this channel. You've helped me since 10th grade and I'm now in my 2nd year of my civil eng. degree taking calc 4. I appreciate it dawg
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..
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. 🙂🙂
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
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)
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?
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 😁
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.
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.
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 ;)
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|.
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!
Differential Equations: www.video-tutor.net/differential-equations.html
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!
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?
Organic Chemistry tutor is the OG, better explained videos than most of my university classes on basically every subject
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
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❤
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
Blackpenredpen explained it well
Me 3 years later looking for one 😅
@@nadooalaa1675me too😅
math sorceror has a goated video on it
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
This man has helped me in so many ways. Absolutely grateful.
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
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?
You are one of the reasons I survived first year of engineering. Thanks man !
I almost never comment, but I thought it was worth it to thank you, now i dont think I'll fail my exam!
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
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 facing numerous problems in D. Es but this guy made my life simple
Please watch Professor Leonard Differential Equations Playlist. This professor is awesome.
Thanks man I Got my maths marks 1st Sem, 2nd Sem and i have Grade A for both. Thanks again GOD! Love from SL!
Thank you bro. Six years later this video is keeping on teaching and supporting math students😊
Everytime I see that you have a video on a topic, I become relieved to know that I will easily understand the topic.
All the way from Kenya thanks for making my school life easier .More power to you
He deserves all the tuition money i give to my uni
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.
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
Same😢
10:47 pro tip: you can also replace x=vy ; dx=vdy+ydv, makes the solution easier and shorter
bro this guy is always so clutch. Better teacher than my professor with a doctorate
I used to hear since secondary school and even now in college I follow you all thanks to you
Please I need a full playlist of differential equation tutorials.
x2
Go to khan academy
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"?!
Once I get my degree and a job I’ll donate whatever extra income I get to this guy
This is where I attend my maths class, Thank you so much Prof J.G
The equations must have same dimensions for them to be homogeneous. Great work. Thanks.
how to live life without this man !!!!!!
Good luck my fellow engineering students! You and I will both need it :)
Great video.
All time when I fall in pressure,your video help me,sir.
Thank you very much for your video.
You deserve accreditation. Your education videos are university level.
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
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.
i'm dropping my first pay as a donation as soon as i graduate, you deserve it.
Been here since jhs ✊🏻🖤 and now I’m surviving college, thanks alot sir!
U r a breathe of fresh air. Thank u
Preparing for my end of semester paper in a few hours. Thanks King!
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!
I'm a mechanical engineering student and let me just say that not all heroes wear capes❤... My organic chemistry teacher 🎉
I should be paying my whole school fees to this guy rather than my current institute
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 :)
Your talent will remain as rememberance dear Thanks to almighty father n continues increasing your incredible thought 💖🔥
I'm speechless. Cryatal clear explanation
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 😂 👏🏻
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.
You are the king bro❤️ i always come back to clear concepts from your videos from school to grad. Thanks man❤️
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 can write it like that as well so the opposite would be [Ln(1-v)]^(-1)
This man is doing the Lord's work😂
Thanks man for making computer engineering manageable for me
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!
It's amazing that you make video on everything I need.
Ay bro imma drop a mad amount on this channel. You've helped me since 10th grade and I'm now in my 2nd year of my civil eng. degree taking calc 4. I appreciate it dawg
same here
thank you for always showing all the simplifying steps
Major respect......watching this during quarantine and im absolutely enjoying it!
QUARANTINE FREN HAHA
Is there a nobel prize for this guy? cuz we gotta give it to him
Studied from this channel in my 10th now I'm back.. Currently doing Btech
I just want to say from the bottom of my heart, I love you and I will always love you.
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..
Sir,love your lecture so much..💖💖💖
Thanks & respect from the deepest core of my heart..
Great content buddy
As an economics major who had mathematics as his minor your content really helps me
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?
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
Thank you for teaching me, learning online really tiresome but with your videos make me understand it✨🤌🏻🤌🏻
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
Thank you Sir you are the best
#RespectFromSouthAfrica
saaaaaaaaaaaaaaaaaaame
can someone please explain the first example isn't that a linear first order equation , so can we use the integration factor method?
Thanks from India
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)
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?
Woow great staff my brethren may God guide you jealously for me,
Thanks my guy. Feeling confident
Bro has a patreon for those who are feeling generous
I would like to donate to your channel as well. Great work
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).
THANK YOU. I HOPE I CAN ANSWER THE QUIZ ON HOMOGENEOUS.
Thank you sir, for you wonderful discussion, I hoped that I passed my midterm exam by watching and listening to your video.
It is very easy, but it takes some time to solve it, thanks for the help
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.
26:30 Shouldn't we use ln in the last equation and seperate y/x so it stays only y=....?
I love this channel
Man! Thank you a lot for your videos. So well explained that you make it easy. Kudos my man ❤️🙏
the man the myth the legend
This is very helpful in so many ways! Thanks a lot
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
more vids about differential equations pls i like the way you teach
in 26:12 you ve missing the 2 of constant c when you clear up the screen :)
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 ;)
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 :(
❤❤❤❤❤very understandable..thank you very much
This gave me anxiety.
You did great, but this is tedious lmao
youre right
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!
Can you make a video on the reduction of order method for 2nd-order differential equations
my life line my pookie my everything thank u man
Hi , loves from india . You r an OG ❤❤
I appreciate you work man 🤧