Math 391 Lecture 3 - The integrating factor method and homogeneous 1st order ODEs

In this lecture, we continue to discuss ways of solving various first order ODEs, which is the focus of chapter 2 of Boyce/DiPrima. We focus our attention first on first order linear ODEs, in particular, those that are not separable. We look at the method of integrating factors to solve such equations, after deriving what the needed integrating factor must be. We then move on to homogeneous differential equations--a bit of a misnomer, since we will see later that "homogeneous" usually refers to something else--but we look at ways to turn such equations into separable ones with a powerful substitution technique. We did several examples of applying the integrating factor method here, but only one example of dealing with homogeneous 1st order ODEs; we will pick up with more examples next time.

[NewJayqwe]

You are soo amazing, for weeks I didn't understand this but with your I understood completely immediately, wish I found you sooner :3

[azfam]

those vids were very helpful a night before the test. thanks very much all the way from saudi arabia.

[mustafaabdi]

Great and easy to understand, thank you so much for making these videos you helped me much. :D

[maguiar]

Thanks for sharing your lectures with us, professor. It's helping me a lot! :)

[countingpebbles]

My friend, 26:40 can be solved by separation of variables, I did it and got the same answer!

[erickrobles]

Hi Jhevon, why is it that we don't add the [+C] on the side where we did the partial fractions? Thanks again!

[swanhtet]

How can you/we notice if an expression is separable or not just by looking at it?
You do it pretty fast. Are there any thing that hints that it is separable or not (without testing it literally) ?

[mudasirjan]

5:25 He in fact, did not “see it now”

[smoothsmith]

@57:50 i have no idea how you got ln|x|^-4

[Gmaraio]

Lol you can't spell "separable"