Solving a first order linear diff eq (integrating factor, method of undetermined coefficient)

0:00 use integrating factor
6:47 undetermined coefficient

[BALAGE]

"Linearly independent, which means that they have nothing to do with each other." I like that, straight to the point.

[aryankhemka]

Hey! I just finished watching your 6 hour video on solving 100 integrals! Definitely boosted my confidence for integration which will help me in my upcoming exam!

[GaryTugan]

liked them BOTH :) I love to do these problems first, and then watch how you do them... always pick up SOME detail that is pretty slick. Appreciate your vids!

[Alex-lixh]

Thank you for the explanation, I use the first method but I liked the second method, have a nice day :)❤

[alejrandom]

15:41 I love how he first says "dont we?" But then remembers he's bprp 😁

[tomatrix]

Hi steve, your videos are very fun and interesting. They have improved my maths aswell

[chritophergaafele]

You are the best online Calculus Teacher

[nrrutube]

Method 2 was mindblowing I don't think I've ever seen that before, I'll have to try and remember it for the future!

[UAa]

I love your videos sir and your microphone it's cool.

[SmerFable]

I have differential equations exam at this week, thank you so much for that video!

[lesnyk]

Method 2 confused me at first because the homogeneous equation in your example is separable, and much more easily solved directly. Then, in the middle of composing a long question to you about It, I remembered how you need the auxiliary equation to solve higher-order linear Diff-E's with constant coefficients. (It's been 50 years since I studied this stuff.) So, yeah, Mehod 2 CAN be applied to 1st order - but it's most useful for 2nd order & higher.

[roderickwhitehead]

I am going back over 15 years now... but I seem to recall that in my junior year of a Mechanical Engineering curriculum, towards the end of Differential Equations, we were using Laplace Transforms for these type of first order differential equations... and concurrently, in Kinematics or maybe it was Machine Design we were being taught to solve using Laplace Transforms. It was very frustrating to be completely traumatized by nearly a whole semester of Dif. EQs... only to be given the tools we were actually going to be using in our 400 level M.E. classes... as what seemed like an afterthought.

Fast forward 15+ years... and I still struggle with this stuff.

[warryen]

Last year me was lazy, but happy to have you before my exam time. This year me is going to be proactive, and happy to have you before my class. :)

[Lamiranta]

Hi bprp. Thanks for explanation. I think my math's level increase very fast with your videos. And I have next question: can you help and solve the integral from 0 to 1 of sin^-1(x)/(x^2+x^(4/3))dx? Good luck and make more videos!

[nvapisces]

Thanks for the video. Wish H2 math also have such stuff

[Abdopro]

thank you (from moroco ) you are the best

[ComplicatedButSimplified]

That is why method 1 is taught in schools as it's small but method 2 is also interesting

[tylerbrown]

Integrating factor is the easiest by far. The other method would require superposition. In superposition, both parts of the right side could be done with undetermined coefficients, but adjusting the parameters would also work with a little more work.

[erickjoshuanebreja]

bprp what if the mu(x) has a y variable in it?

[zmaxic]

Are you sure if superposition method will always work?
How about the variation method of an arbitrary constant?
How about the Bernoulli method?