# Solve the given differential equation by separation of variables. (dy)/(dx)=(x^2 y^2)/(1+x)

Solve the given differential equation by separation of variables.
$\frac{dy}{dx}=\frac{{x}^{2}{y}^{2}}{1+x}$
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Sandra Randall
$\frac{dy}{dx}=\frac{{x}^{2}{y}^{2}}{1+x}\to \int \frac{dy}{{y}^{2}}=\int \frac{dx}{1+x}$
$-\frac{1}{3}{y}^{-3}=\mathrm{ln}\left(x+1\right)+\mathrm{ln}\left(c\right)=\mathrm{ln}\left(c\left(x+1\right)\right)$
${e}^{-\frac{1}{{y}^{3}}}=c\left(x+1\right)$