I want to solve $M$ where $M(t)$ is a function of time $t$. I have this equation, $$M'(t) = - \mu M(t) + \alpha M(t) e^{-\beta M(t)}$$ where $\alpha, \mu$ and $\beta$ are nonnegative constants. I know that I need to take the integration in order to do so but I do not know how to solve it. I already tried integration by parts but it gives me a much more complicated equation after. Can someone tell me what technique to use?
Thank you very much in advance.