I'm asking this question on behalf of another person who is not as familiar as me with computers. He has the following problem to solve and unfortunately Mathcad can't solve such type of equations.
He seeks help to find the function $u = u(x) = ?$ for
$ \frac{d^2u(x)}{dx^2} =\left[U(x) + \alpha^2\right]u(x) $
where $U(x) = \frac{2}{x}\left(\exp\left(-\frac{x}{\lambda}\right)-\int_0^x 4\pi\left(u(z)\right)^2\,dz\right)$
The parameters $\lambda$ and $\alpha$ are real.
Is another tool (i.e. Mathematica) able to solve it ? Do you have another suggestion ?