Using ODEs in projectile motion

Question

If a cannon fires a cannon ball, where the only other forces are gravity and friction (denoted $pv$, where $v$ is velocity and $p$ is a constant), what would the horizontal equation be in terms of ODEs? Would I be right in assuming $m\frac{d^2x}{dt^2}+c\frac{dx}{dt}=0$?

Answer 1

HINT: make the ansatz $$x(t)=e^{\lambda t}$$ and plug this in your equation