Question: help Solve stiff nonlinear DAEs with unknown initial boundary conditions

 Hi,

I have the following set of equations and boundary conditions. The problem is I cannot be able to make accurate guesses with the shooting method. I request your assistance. 

> 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];

M=[0..10], b=[-0.5..1], Du=[1..2], Sr=0.15, Sc=[0..3], Ec=(0,1), Lambda=[0.1..1], Pr=0.71,

eta=eta+(small change in eta)on each iteration loop.