If I have an Euler-Lagrange equation: (y')^2 = 2 (1-\cos(y)) where $y$ is a function of $x$ subjected to boundary conditions $y(x) \to 0$ as $x \to -\infty$ and $y(x) \to 2\pi$ as $x \to +\infty$, how might I find all its solutions?
I can't seem to directly integrate the equation and sub in the conditions... Please help!
Thanks.