Question

How to integrate dy/(y-x^3)?

Answer 1

These are the questions where we pretend x is a constant right?

Answer 2

That is what I have to assume since nothing is given about x in terms of y

Answer 3

do you know how to evaluate:
\[\int\limits_{}^{}\frac{dy}{y-5}\]

Answer 4

hint if you can back:
\[\frac{d}{dy}(\ln|y-constant |)=\frac{1}{y- constant }\]

Answer 5

Oh~, I got it! I forgot that we have to treat x as constant.

Answer 6

Thanks!

Answer 7

np

Answer 8

@Idealist10 I suspect you're still trying to tackle solving the ODE from before: http://openstudy.com/users/idealist10#/updates/54e646ebe4b00fdbfc1770fa

This attempt to integrate will not work!

Answer 9

... by which I mean you won't get the correct solution.

Answer 10

oh yeah that will not work

Answer 11

I'm sorry
I didn't know this was part of a bigger question

Answer 12

It might not be, I just have a feeling about it... In the case it is a different question (not ODE-solving-related), the integration would be carried out as above.

Answer 13

\[-x^2=y'-\frac{1}{x} y \\ -x^3=xy'-y \\-x^3+y=xy' \]
it kinda looks like it though

Answer 14

\[y'-\frac{1}{x}y=-x^2 \\ \text{ integrating factor }=e^{\int\limits \frac{-1}{x} dx}\]

Answer 15

@SithsAndGiggles , I know it won't work. I just found out that it won't work before you guys answered the question about integrating dy/(y-x^3). But I solved that ODE problem already, in the middle of that ODE problem, I found an exact derivative and I solved it successfully. So don't worry about it anymore.