$\frac{\mathrm d^2y}{\mathrm dt^2} + p\frac{\mathrm dy}{\mathrm dt} + qy = 0$
If the eigenvalues are complex, what conditions on $p$ and $q$ guarantee that solutions spiral around the origin in a clockwise direction ?
I found the eigenvalues to be: $\lambda = -\frac{p}{2} \pm \frac{\sqrt{p^2 - 4q}}{2}$
and not sure how we can answer this. All I note that if $p > 0$ and $p^2 - 4q < 0$, then we have a spiral sink. How does it help me if I can get conditions for spiral sink or source and match their directions (counterclockwise or clockwise) when the problem indicates we are able to do this without the use of technology sketching a phase portrait?