Solve the ODE:

$\displaystyle \frac{dy}{dx}=-\frac{y}{\sqrt{a^2-y^2}}$

3. The attempt at a solution

My teacher hinted that the substitution $\displaystyle z^2=a^2-y^2$ could be helpful, but once I make the substitution, I can't seem to take the next step.

$\displaystyle z^2=a^2-y^2$

Differentiating WRT x, we have:

$\displaystyle 2z\frac{dz}{dx}=-2y\frac{dy}{dx}$

Substituting back in we have:

$\displaystyle \frac{dz}{dx}=\frac{a^2-z^2}{z^2}$

But I can't take it from here... much less obtain an equation for y(x). Any thoughts?