Integrating factors question?
Okay I have this question. I will just type myu (the Greek letter) as m.
So guys I was looking at examples of integrating factors and on youtube this person said that it doesn't matter whether you pick m(x) or m(y) or m(x;y). But if I pick any of them, will it change my answer, or will it not allow me to solve the differential equation? Because on the test, say I pick m(x) and try solving for it, first, I don't want to waste time, if for example my equation would be easier to solve if I picked m(y), and second what if it gives me wrong answer? So is there any way
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to know whether I should pick m(x) or m(y) or m(x;y)?? It's like integration by parts, where you pick the u to be a function, that if you differentiate, it will eventually become 0 (example in x*e^x, u =x, dv = e^x). So I was wondering if you can know in terms of what variable to pick myu, so as not to waste time on the test.
Okay I know how... Just found this:
If (My-Nx)/N is a function of x only, then we find integrating factor μ as follows
μ = e^(∫ (My-Nx)/N dx)
If (Nx-My)/M is a function of y only, then we find integrating factor μ as follows
μ = e^(∫ (Nx-My)/M dy)