ok i have a question im really stuck on

for this i used the substitution u = x^3y and end up with but no matter how i rearrange it i cant separate the variables

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- February 14th 2010, 04:56 PMrenlokan ODE question
ok i have a question im really stuck on

for this i used the substitution u = x^3y and end up with but no matter how i rearrange it i cant separate the variables - February 14th 2010, 05:12 PMJhevon
- February 14th 2010, 05:18 PMANDS!
Oh dear. Well, at least you recognize this as a linear first order differential. It is the confusion on what your integrating factor is that is the problem. Remember, a differential is in linear form when it is written as:

, with an integrating factor equal to .

Rewriting the equation so that it is in linear form we get:

Thus, our integrating factor is . From here you should see how things start to cancel out. If you need more help, post here. - February 15th 2010, 08:58 AMJhevon
the ODE is already in the required form. if we do what you did, we'd end up with , and multiplying through by that brings us back to the original ODE! we don't need an integrating factor here, everything is already in a nice form. just continue as if you already found the integrating factor