The general solution of the differential equation

$y\left(x^2 y+e^x\right) d x-e^x d y=0$, is

$x^3 y+3 e^x=3 C y$

We have,

$y\left(x^2 y+e^x\right) d x-e^x d y=0$

$\Rightarrow x^2 y^2 d x+y e^x d x-e^x d y=0$

$\Rightarrow x^2 d x+\frac{y e^x d x-e^x d y}{y^2}=0 \Rightarrow x^2 d x+d\left(\frac{e^x}{y}\right)=0$

On integrating, we get

$\frac{x^3}{3}+\frac{e^x}{y}=C \Rightarrow x^3 y+3 e^x=3 C y$