I recently solved a differential equation for a body in free-fall. $$\frac{dv}{dt} + \left(\frac km\right)v = g$$
This is first-degree, non-separable with an integrating factor.
However, most physicists know that the fluid drag $\left(\frac km\right)v$ goes as the square of the velocity. The equation takes the form: $$\frac{dv}{dt} + \left(\frac km\right)v^2 = g$$
How do you solve this equation, and what type is it? It doesn't appear to be a "Bernoulli".