Solution of the differential equation $y (2 x y + e^{x}) d x - e^{x} d y = 0$ is .....

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Solution

$\begin{matrix} y (2 x y + e^{x}) d x - e^{x} d y = 0 y (2 x y + e^{x}) d x = e^{x} d y y (e^{x} d x - e^{x} d y) + 2 x y^{2} d x = 0 D i v i d e b y y^{2} \frac{e^{x}}{y} d x - \frac{e^{x}}{y^{2}} d y + 2 x d x = 0 \frac{y e^{x} d x - e^{x} d y}{y^{2}} + d (x^{2}) = 0 \frac{e^{x}}{y} + x^{2} = C \end{matrix}$

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