Nonlinear differential equation gone beyond my field of expertise but I'd like to know the details of a problem and to do that I should know the general solution of the following nonlinear differential equation:
$$y'(x) = \alpha\beta e^{-\frac{x}{\gamma}} - \delta \sqrt{y(x)}$$
with $\alpha, \gamma, \delta > 0$ and $0 \leq \beta \leq 1$. Since $x$ represents the time is it also possible to assume $x \geq 0$.
I tried to solve it with Wolfram Alpha and Wolfram Mathematica but I didn't get any result due to computational time excedeed.
Is it possible to find an analytical form of $y(x)$?