Differential Equation Question :)

Use the substitution y=vx where v is a function of x to find a general solution of

dy/dx=(x^2+y^2)/x(x+y)

What I have so far; dy/dx=v+xdv/dx

By substitution v+xdv/dx=(x^2+(vx)^2)/(x^2+vx^2)

cancel out the x^2 on RHS v+xdv/dx=(1+v^2)/(1+v)

xdv/dx=(1+v^2)/(1+v) -v(1+v)/(1+v)

xdv/dx=(1-v)/(1+v)

(1+v)/(1-v).dv=(1/x).dx

I rearranged LHS to -1 + 2/(1-v)

Integrate both sides -v-2ln(1-v)=lnx + c where c = lnA

And from here I need to get to

y=xln((Ax)/(x-y)^2) where have i gone wrong and/or what do i do now??

Cheers :smile:

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