I'm working on solving a separable first order differential equation where I get down to:
$$\frac12 y^2 + e^y = \frac12x^2 + e^{-x} + c$$
Is it possible to solve for $y$ here? I can't think of a way to factor the left hand side.
Here's the original differential equation:
$$\frac{dy}{dx} = \frac{x-e^{-x}}{y + e^y}$$
Thanks!