@PatrickT

 Hi Dr.,

Thanks for your reply.  

The unknown boundary conditions   X[2](0) = S[1],  X[4](0) = S[2],  X[6](0) = S[3], are to be estimated using the shooting method employing 4th-order Runge-kutta method whereby,

diff(X[1](t), t) = X[2](t), diff(X[3](t), t) = X[4](t), diff(X[5](t), t) = X[6](t);

My problem is how do you create this "recall/loop" and develop a rapidly converging algorithm as these differentials are part of the equations to be solved as well as estimates to boundary conditions.

Solve the 3 difference equations and estimate the boundary conditions from the exact solutions obtained-(My understanding for the shooting method) 

Then plot while some parameters are varied like M.

Thanks.