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## Homework Statement

Solve (xy+y

^{2}+x

^{2}) dx -( x

^{2})dy = 0

## Homework Equations

to verify if exact

**[PLAIN]http://upload.wikimedia.org/math/5/2/c/52cc749bb1c32abf1dccf613bd847a6e.pngM/[B][PLAIN]http://upload.wikimedia.org/math/5/2/c/52cc749bb1c32abf1dccf613bd847a6e.pngy [Broken] =**

**[PLAIN]http://upload.wikimedia.org/math/5/2/c/52cc749bb1c32abf1dccf613bd847a6e.pngN/[B][PLAIN]http://upload.wikimedia.org/math/5/2/c/52cc749bb1c32abf1dccf613bd847a6e.pngx[/B][/B][/B][/B] [Broken]**

So I can see it isn't separable and linear, so I thought of solving it through substitution

i did y=ux and dy= u dx + x du

and I substituted them in my first equation giving me

(xu+u

I'm stuck here... the answer key factors out x^2 from the first equation leaving it with x^2(u+u^2+1), which doesn't make sense to me.. because if I factored out x^2 I would be left with (x

So any help on how I am seeing this wrong?## The Attempt at a Solution

So I can see it isn't separable and linear, so I thought of solving it through substitution

i did y=ux and dy= u dx + x du

and I substituted them in my first equation giving me

(xu+u

^{2}+x^2) dx - x^{2}(udx + xdu) = 0]I'm stuck here... the answer key factors out x^2 from the first equation leaving it with x^2(u+u^2+1), which doesn't make sense to me.. because if I factored out x^2 I would be left with (x

^{-1}u+x^{-2}u^{2}+1)So any help on how I am seeing this wrong?

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