I have the following 1st order equations and need to solve them using Maple 12. There are unspecified initial conditions and can only be estimated through the Newton raphson method. My problem is how do I implement it so that the equations are numerically solved using rk4-order. Tried out with BVPsolve but doesn't work. this is in line with works by Makinde. "On MHD boundary-layer flow and mass transfer past a vertical plate in a porous medium with constant heat flux."
> k1 := diff(X[1](t), t) = X[2](t);
> k2 := diff(X[2](t), t) = M*(X[1](t)-1)-(2*(eta+b))*X[2](t);
> k3 := diff(X[3](t), t) = X[4](t);
> k4 := diff(X[4](t), t) = (2*Sc*Du*(eta+b)*X[6](t)-Du*lambda*X[5](t)-2*Pr*(eta+b)*X[4](t)- Pr*Ec*X[2](t)^2-Pr*Ec*M*(X[1](t)-1)^2)/(1-Du*Sr);
> k5 := diff(X[5](t), t) = X[6](t);
> k6 := diff(X[6](t), t) = (lambda*X[3](t)+2*Pr*Sr*(eta+b)*X[4](t)+Pr*Sr*Ec*X[3](t)^2+Pr*Sr*Ec*M*(X[1](t)-1)^2-2*Sc*(eta+b)*X[6](t))/(1-Du*Sr);
> ICS := X[1](0) = 0, X[2](0) = S[1], X[3](0) = 1, X[4](0) = S[2], X[5](0) = 1, X[6](0) = S[3];
