# Solve. dy/dx = xy(1-y)

Solve. dy/dx = xy(1-y)
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dy/dx = xy(1-y)
dy/[y(1-y)] = xdx
$\int \frac{1}{y\left(1-y\right)}dy=\int \left[\frac{1}{y}+\frac{1}{1-y}\right]dy=\int xdx$
$\mathrm{ln}y-\mathrm{ln}\left(1-y\right)=\frac{1}{2}{x}^{2}+C$
$\mathrm{ln}\left(\frac{y}{1-y}\right)=\frac{1}{2}{x}^{2}+C$
$\frac{y}{1-y}={e}^{\frac{{x}^{2}}{2}+C}=D{e}^{\frac{{x}^{2}}{2}}$