Help solving this differential equation

Hey there i'm looking for a solution to the following non-linear first order ODE.

$(\frac{dy}{dx})^2 = Ae^{-y}+By+C$

where A, B and C are constants.

Any ideas on how to solve this or if it's even got an analytical solution?

As to whether this has an analytic form, I fed an example of an equation of this form to Mathematica, and it went away and thought for a while and returned with a simple re-write of the original equation. So, possibly not...

Hey there i'm looking for a solution to the following non-linear first order ODE.

$(\frac{dy}{dx})^2 = Ae^{-y}+By+C$

where A, B and C are constants.

Any ideas on how to solve this or if it's even got an analytical solution?

Isn't this equivalent to $\pm \int \dfrac{dy}{\sqrt{Ae^{-y} + By +C}} = x+D$? The integral doesn't look at all hopeful for a solution in terms of elementary functions.

Yup, that is what Mathematica returns...

Isn't this equivalent to $\pm \int \dfrac{dy}{\sqrt{Ae^{-y} + By +C}} = x+D$? The integral doesn't look at all hopeful for a solution in terms of elementary functions.

I will try a numerical method