Solve ODE of form y''+(2/x)y'=C*(e^y) where C is a constant
The Attempt at a Solution
I don't really see how to approach this one, so a point in the right direction would be great.
I was trying to solve del^2(Psi)=Ae^(Psi) in spherical polars, for the radial component.Where did you get this problem from ? I'm almost sure there's no analytical solution (Mathematica couldn't find any combination of elementary/special functions which would satisfy the equation) to it, so an approximate solution would be the best you could ask for.
Thanks alot for your help. The question does say that Psi varies over a length scale that is approximately the same as the region which I'm supposed to be analyzing. Does that somehow mean I can take the RHS as constant?Yes, it looks correct. However, my guess is that the nonlinearity in the RHS spoils the <neat> intregrability.