First Order Linear Differential Equations
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- Опубликовано: 1 окт 2024
- This calculus video tutorial explains provides a basic introduction into how to solve first order linear differential equations. First, you need to write the equation in standard form [y' + P(x)y = Q(x)] and then identify the functions P(x) and Q(x). Next, you need to determine the integrating factor I(x) using the formula I(x) = e^(integral of P(x)dx). Finally, you can use another formula to find the general solution of the first order linear differential equation y = 1/I(x) [Integral(I(x)Q(x)dx + C]. This video contains plenty of examples and practice problems on solving first order linear differential equations.
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Pls can you tell me what textbook you used for these, I think my lecturer is using same thing because the questions and solutions are all the same
at university: wtf... on youtube: bruuuh that's it?
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This is high school
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You took the words right outta my mouth lol
I've been struggling with differential equations and in just a few minutes you made everything click. I honestly don't understand why university lecturers don't include a simple "and here's the actual steps you need to take to solve an equation like this" after all of the heavy theory.
exactly, theory pisses me off
@@telamporen5680 Nothing is wrong with theory, the problem is professors simply can't teach math effectively. Theory is good when you follow it up with simple instructions like organic chemistry tutor. I hate how all throughout life teachers make math look so much harder than it actually is
@@telamporen5680 I think theory is really important to teach, its really frustrating when that's all you're taught and then you're expected to derive the formula manually every single time you do a problem
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It becomes simple after listening what you tech.great. thank you so much.
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Leonard is unnecessary lengthy and chatty. OCT is the epitome of conciseness. Man is talented,
@@anycolouryoulike8567 prof leonard goes into a lot more detail though. These videos by OCT are only to supplement an actual lesson. They dont get into any of the reasoning behind why or how this works
@@brandonbennett4970 Maybe, but he gives just enough information to get high exam scores.
Yeah like he doesn't talk why something happens , probably he's a student as well and not a full blown professor , even I taught students once when I was in University [ economics to high school peeps ]@@brandonbennett4970
@@brandonbennett4970 yes unnecessary derivation, my favourite
u lost me at 0:02
Wow
I'm not sure how my actual professor made this SO much more complicated while she was teaching it during lecture lol wtf
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00:00 -how to
01:13 -prob1
04:28 -prob2
10:24 -prob3
18:58 -prob4
thank you
Thanks
13:41 - prob 4
Not the hero we deserved, but the hero we needed
you really out here teaching me things better than my teachers lol
when you quickly finish the solution before he does, and earn some free time to slack off
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This is way easier than what my book was trying to make me do. Thanks a million, as always :)
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@@Alexis.645 there was no point. A point is a logical fact. It was a joke and I mentioned it as one in my previous comment
I got the highest score in our examination thanks for your help
I learned ODE in late 1960, 50 years ago, never came across this topic. Now I am over 70 years old, still enjoy learning this. Thanks very much for this simple and elegant explanation!
What was your favorite decade and why
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Thank you for doing multiple and different examples. I feel like my professor teaches the concept and doesn't show many examples. You are the basis of my learning in depth.
As is tradition at this point for all struggling engineering students, I have a final exam in 12 hours and plenty to cover. May your voice, skills and talents continue to liberate us in Jesus' Nam'e. Amen
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In the last example, you can simply separate the equation (x² - y)/x into two terms: x - y/x. Goes the same answer, sir.
Nonetheless, thank you so much for this vid! you've been my comrade since my first year in college.
Perfect explanations and flawless teaching. Brilliant examples too.
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for the last problem, you can simply spit apart the fraction and make it x^/x and -y/x. then I added y/x to both sides and got dy/dx +y/x = x^2/x. This leaves you with a P(X)= 1/x and a Q(x)= x as well.
I have been watching you since my first year of college and you are probably the only reason why I passed any of my math classes
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Super interesting video! I have a question though, why I(x) doesn’t have a + C when you integrated P(x) dx?
Not all hereos wear capes
For the last example there's a much quicker way to get it into standard form. Re-write (x^2-Y)/X as X^2/X - Y/X and the just add the Y/X term to the left side.
Can anybody explain to me the 2nd last and last question on how to check whether it is correct?
By putting the answer back into the standard form.
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What I understood by reading a book for 3 hours, this guy explains differential equations clear cut in 25 minutes, thank you immensely. ❤❤
Very Helpful, thank you very much
11-02-2022 | Math 202 | @ Al Hassa
Question. shouldn't we consider absolute value when it comes to ln? e.g. instead of ln(x-2), it should be ln|x-2| ??
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jesus. at 16:38 you said e^lnx^4/5 = 4/5. it caused me to go full on frantic mode for 30 mins finding out why.
But thank you so much. you really saved my exams
how is it equal 4/5?
lol, I paused it, just had to watch a bit more
why integral of 4 over x is x power of 4? I thought that there should be ln(4x)
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I wish you had a full differential equations playlist cause your videos are great for it.
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-_- so this is it? What's wrong with university lectures bruhhh
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i've been staring at my lecturer's calculation for a very long time and i till can't figure it out why the answer got like that. then i know i always have to go to you, you almighty
Professor Organic Chemistry Tutor, thank you for another fantastic video/lecture on First Order Linear Differential Equations. Introductory Differential Equations books use a different method to solve First Order Linear Differential Equations. Many Introductory Differential Equations books after finding the Integrating Factor, use it to multiply the standard form equation and then solve for y. This is an error free video/lecture on RUclips TV with the Organic Chemistry Tutor.
Love the way you explain each step
Easy to understand
Keep up the good work
I wish you could make more videos about differential equation
You help us to see the things we can’t see ordinary…… you make us bisect these concepts to the deepest parts of understanding…. We thank you sir
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Do you mind we connect, I love sharing ideas especially on Mathematics
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Bro ASU math needs to pay you because you teach this better than any of their professors jfc
For real though
why do you take the ln|x-2| as just ln(x-2)?
you can't have a logarithm of a negative number, no?
Only our weak-ass teachers disliked this video.
waahhh. I'm not sure how I'd ever have understood differential equations. thank you sir.
You're a lifesaver. Thanks a lot. I hope now I can pass my test tomorrow. Keep up the good work.
Verbal mistake on 10:07, “14/2 is 2”
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@ 2:08 "That's going to be e times the integral of...." I think you meant to say "raised to the...." Am I right or wrong? Just trying to understand here... TY
Sir,
You have explained the solution of linear differential equation in a very nice manner.
In IIT-JEE Mains 2019 , 10 Jan, shift1, there was a question " if (integral ( limit 0 to x)) f(t) dt = x^2 + (( integral limit 1 to x ) ( t^2 * f(t)) dt) then f'(1/2) = "
For the solution of this question, the differentiation of definite integral wrt x is done. The process is not clear.
Please, prepare a detailed video.
anybody know what to do when q(x) is zero?
Why don’t we add the constant in the integration which is the index of e? I’d love a mathematical proof as i tried calculating one equation with and without c in the index, giving me results of only one new constant at the end, but I’m not very sure if that is enough to cover the whole story and may be improper for particular equations.
Sir pls upload Linear differential equations:
- Operator D
- Rules for finding the complementary function
- Inverse Operator
- Methods for finding the particular integral
- Working Procedure to solve the equation
- Two other methods of finding P.I.
- Equations reducible to Linear equations with constant coefficients
- Linear dependence of solution
2024? Anyone 😂
you save my life. Thank you very much
I notice that the usual method after getting I(x) is to multiple it on dy/dx and Q(x). Then you integrate both side, then try to get Y=f(x). But this video showed a much simpler solution which is 1/I(x)[integration of p(x)Q(x) dx]. And i want to know how you got it in this equation
Paused at 16:32. Thought to self =(. I could have sworn... I mean... Did I learn wrong all this time? =(. But how? But why? Calculus fails me again! Let me just keep on going through then =(.
when i graduate electrical engineering, ill print a copy of my graduation certificate In his name.
We have nothing to pay u back!!🙏
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Please keep making videos about these topics :"(
Who's here because they have no clue what the prof is talking about? I know I am, and this explains the subject so well universities really should hire this man to be a professor. Give him a PhD in education or something idk.
bro wtf, this video summarized what our teacher explained in 2 hours + 30 pages to read. is it really that important that our teacher explains every f*** theory and proof behind every arithmetic computation.
For the last Question , cant we just divide only the right hand side by x from the start and since in the end we still get the same p(x) and q(x)
No, we also need to add Y
He made a mistake on the last question... he said both p[x] and q[x] were equal to x hence p[x] =1/x
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At 12:19 why didn't you put the absolute amount in brackets? As Log can only be taken from positive numbers. Is it because e ^ ln are eliminating themselves already?
I'm here to advance studying this topic for next school year. I thought this topic could be hard but when I watch this shuxxsxx how could be easy for him to teach this in just minute I understand it properly than to my prof last sem tbh...
organic chemistry is my fav teacher but I cant understand what happened in the first minute of the video can anyone provide a reference material how he figured out the integrating factor and y = 1 / Integrating factor, what is just happening😵💫
just sit like a dumbass on the classroom when prof is giving lecture.....but here omg.....bro you are really awesome.... wish you were my university teacher
late to the party guys, but a supplemental book to this lecture would be ken stroud's engineering, its stuff at the end of the book like this really builds a solid foundation for laplace/fourier stuff as well as partial ODE's
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