Hi everyone

Need help to verify this working,thank you in advance for all your kind help & support.

$\displaystyle x^2\frac{dy}{dx}=y^2+2xy$(Hint:Substitute$\displaystyle u=\frac{y}{x}$

$\displaystyle \frac{dy}{dx}=\frac{y^2+2xy}{x^2}$

$\displaystyle u+x\frac{du}{dx}=u^2+2u$

$\displaystyle \frac{du}{u(u+1}=\frac{dx}{x}$

$\displaystyle \int(\frac{1}{u}-\frac{1}{u+1})du=\int \frac{dx}{x}$

ln|u|-ln|u+1|=ln|x|+c

$\displaystyle ln|\frac{\frac{y}{x}}{\frac {y}{x}+1}=ln|cx|$

$\displaystyle \frac {y}{x+y}=cx$

y=cx(x+y)

Thank you in advance.