Let's say I have a set of nonlinear differential equations of the form. [tex]x' = f(x,y) \\ y' = g(x,y)[/tex] Where f and g contain some parameter 'a' that is constrained to within certain values. Let's say I know x(0), y(0) and x(T), y(T) where T isn't a set value. What methods can I use to solve/integrate this to match the boundary conditions with the parameter 'a' free to change. I suppose if T could be minimized that would be nice but it's not essential, just looking for general methods used to solve these sort of problems.