The general solution of the differential equation $y\left(x^{2}y+e^x\right)dx-e^{x}dy=0$, is

We have,

$\begin{array}{l} y\left(x^{2}y+e^x\right)dx-e^{x}dy=0\\ \Rightarrow x^2{y}^{2}dx+y{e}^{x}dx-e^{x}dy=0\\ \Rightarrow x^{2}dx+\frac{y{e}^x}{y}\frac{dx-e^x}{y^2}\frac{dy}{y}=0\Rightarrow x^{2}dx+d\left(\frac{e^x}{y}\right)=0\end{array}$

On integrating, we get

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