Solve by separation of variables: $\frac{dx}{dy}y\ln|x| = \big(\frac{y+1}{x}\big)^2$

Question

I need to solve the problem above using separation of variables. I got as far as the below but it seems too complex to be right. Am I wrong somewhere? Because I think my final answer needs to simplify to get $y$ alone but that doesn't seem possible...

$$ \frac{1}{9}x^3(3\ln|x|-1)=\frac{y^2}{2}+2y+\ln|y|+C $$

Answer 1

$$ \frac{dx}{dy} yln(x) = \frac{(y+1)^2}{x^2} $$

$$ \int x^2 \ln(x) dx = \int \frac{(y+1)^2}{y}dy $$

$$1/3\,{x}^{3}\ln \left( x \right) -1/9\,{x}^{3}=1/2\,{y}^{2}+2\,y+\ln \left( y \right) $$

I used Maple to do the integration, but you should use Integration By Parts for the first integral and linearity of the integral for the second if you are doing the integrals by hand.