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Integrating factor

by roryhand
Tags: factor, integrating
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Sep25-05, 12:59 AM
P: 2
Howdy, I've read this forum for some time, however this is my first post. I am attempting to solve this ODE. I am looking to find an integrating factor, then solve. I have attached the link to the problem set if my input here is ambiguous. Number 4d. Thank you kindly for any help you might lend.


My reasoning takes me as far as the integrating factor being exp(int( ? )dx)
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Sep25-05, 01:57 AM
P: 109

(2x^2+y)dx + [(x^2)*y-x]dy=0

Now you just need re-read your text-book about how to solve Pdx+Qdy=0, after checking some conditions on P&Q if such an equation has roots or none.
Sep25-05, 03:10 AM
Sci Advisor
HW Helper
P: 1,593
Or can approach it this way:


So, after a quick check for homogeneous, exact, and explicit calc. of an integrating factor via partials, we expand the differentials and attempt to group them together to form exact differentials:


Well, the ydx-xdy can be grouped as:


This leaves us with:

[tex]2x^2dx+x^2ydy+y^2 d\left(\frac{x}{y}\right)[/tex]

Can you re-arrange this now to obtain exact differentials which can be integrated?

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