It is known that ODE boundary value problem is similar to the problem of solving systems of nonlinear equations. Equations are the boundary conditions, and the variables are the values of the initial data.
y '' = f (x, y, y '), 0 <= x <= 1,
y (0) = Y0, y (1) = Y1;
Where y (1) = Y1 is the equation, and Z0 is variable, (y '(0) = Z0).
solve () and fsolve () are not directly suitable for such tasks. Directly should work the package of optimization in relation to a system of nonlinear equations. (Perhaps it has already been implemented in Maple.)
Personally, I am very small and unprofessional know Maple and cannot do it. Maybe there is someone who would be interested, and it will try to implement this approach to solving ODE boundary value problems?