Solution $y=y(x)$ of the differential equation $\left(x^3+2 x y\right) d y=\left(y^2-y x^2\right) d

Question

Solution $y=y(x)$ of the differential equation $\left(x^3+2 x y\right) d y=\left(y^2-y x^2\right) d x, y(1)=1 $ is given by -

Professor PC Thomas Classes · Answer

$\begin{aligned} & \frac{2 x y d y-y^2 d x}{x^2}+x d y+y d x=0 \ & d\left(\frac{y^2}{x}+x yight)=0 \ & \Rightarrow y^2+x^2 y=2 x\end{aligned}$