# Solve differential equation \frac{dy}{dx}= \frac{x}{y}, \ y(0)= -8

Solve differential equation
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curwyrm
$ydy=xdx$
$\int ydy=\int xdx$
$\frac{{y}^{2}}{2}=\frac{{x}^{2}}{2}+c$
Now we use initial condition
$y\left(0\right)=-8$
Substitute the value we get
$\frac{{\left(-8\right)}^{2}}{2}=\frac{{0}^{2}}{2}+c$
$\frac{64}{2}=c$
$c=32$
$\frac{{y}^{2}}{2}=\frac{{x}^{2}}{2}+32$
${y}^{2}={x}^{2}+64$