Find the equations of trajectories for the system $\;\;\dfrac{dx}{dt} = xy$, $\;\;\dfrac{dy}{dt} = -5x$.
I know that the equation $\dfrac{dy}{dx} = \dfrac{\frac{dy}{dt}}{\frac{dx}{dt}}$ is sometimes used to find equations for trajectories in the phase plane, so can I just say that the equations will all take the form:
$\dfrac{dy}{dx} = \dfrac{-5x}{xy} = \dfrac{-5}{y}\;\;$ for varying values of $y$?