What method should I use to solve the equation $\displaystyle (x+y)dx-(x-y)dy=0$ ? It looks like I might need to find an integrating factor to make it exact, but maybe there's a simpler way?

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- Oct 9th 2008, 12:51 AMpetition EdgecombeODE
What method should I use to solve the equation $\displaystyle (x+y)dx-(x-y)dy=0$ ? It looks like I might need to find an integrating factor to make it exact, but maybe there's a simpler way?

- Oct 9th 2008, 01:21 AMshawsend
It's homogeneous. That would seem to be another approach.

- Oct 9th 2008, 02:00 AMpetition Edgecombe
We haven't covered homogeneous equations yet. Is there another way to solve it? There are more problems like this that I am struggling with--they are from page 131 of Elementary Differential Equations (Boyce, DiPrima).

- Oct 9th 2008, 03:23 AMshawsend
Hi. Can't think of one. Standard approach for these is to let $\displaystyle y=vx$, get it in terms of x and v. Separate, integrate, then back substitute v=y/x. Maybe another way though.