I'm having trouble finding the general solution for the following problem:(adsbygoogle = window.adsbygoogle || []).push({});

(1-xy)y' + y^2 + 3xy^3

It's obviously not an exact equation.

I multiply through by an integrating factor (x^m)(y^n) and get

(x^m)(y^(n+2)) + [(3x^(m+1))(y^(n+3))] + [(x^m)(y^n) - (x^(m+1)y^(n+1)]y' (the forms aren't similar, I can't multiply one side to make them similar and have an equivalent equation)

The partial derivative with respect to y:

(n+2)[(x^m)(y^(n+1))] + 3(n+3)[x^(m+1)y^(n+2)]

The partial derivative with respect to x:

m(x^(m-1)y^n) - (m+1)[(x^m)y^(n+1)]

They are not of a similar form so it doesn't do any good to solve

n + 2 = m

3n + 9 = m + 1

What am I missing? Do I need to manipulate the equations somehow?

The General Solution in the book is:

y = [x+-(4x^2 + c)^(1/2)]^(-1) with an integrating factor of y^(-3)

Thanks in advance for the help.

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# Homework Help: Differential Equation

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