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Q.
The solution of the equation $y e^{-x / y} d x-\left(x e^{-x / y}+y^{3}\right)$ $d y=0$ is
Differential Equations
Solution:
The given equation can be written as
$(y d x-x d y) e^{-x / y}-y^{3} d y=0$
$\Rightarrow \frac{y d x-x d y}{y^{2}} e^{-x / y}=y d y$
$\Rightarrow d(x / y) e^{-x / y}=y d y$
On integrating, we get
$-e^{-x / y}=\frac{y^{2}}{2}+c$
or, $2 e^{-x / y}+y^{2}=c$