Pure differential equation whose solution is a siluroid?

Question

I am trying to find a differential equation for the siluroid that DOES NOT contain explicitly $\theta$, $\sin\theta$, or $\cos\theta$, but only $\rho$, $\dot\rho$, $\ddot\rho$. The siluroid equation is $\rho = 4n\cos\theta\cos2\theta$ where $n\in\mathbb{N}$

Thank you in advance.