This is probably really easy, but I am not getting the right answer. Can someone check this please?

Thanks!!

Solve.

$\displaystyle \frac{dy}{dx} = \frac{x}{y}$, $\displaystyle y(0)=-8$

$\displaystyle \int ydy = \int xdx$

$\displaystyle y = \frac{x^2}{2} + C$

$\displaystyle C = -8$

So I get:

$\displaystyle y = \frac{x^2}{2} - 8$

Where am I screwing this up?