(*						      *)
(* Numerical Mathematics and Computing, Fifth Edition *)
(* Ward Cheney & David Kincaid		              *)
(* Brooks/Cole Publ. Co.			      *)
(* (c) 2003                                           *)
(* No warranties implied or expressed.	              *)
(* File: bvp2					      *)

solx = NDSolve[{x''[t] == Exp[t] - 3*Sin[t] + x'[t] - x[t],  
         x[1]  == 1.09737491, x'[1] == 0}, 
         x, {t, 1.0, 2.0}]
soly = NDSolve[{y''[t] == Exp[t] - 3*Sin[t] + y'[t] - y[t],  
         y[1]  == 1.09737491, y'[1] == 1}, 
         y, {t, 1.0, 2.0}]
xb = x[2] /. %1
yb = y[2] /. %2
lambda = (8.63749661 - yb)/(xb - yb)
z[t_] := lambda*x[t] + (1-lambda)*y[t]
Table[N[{t, z[t]} /. {solx, soly}], {t, 1.0, 2.0, 1./11.}]
TableForm[%]
Plot[Evaluate[z[t] /. {solx, soly}], {t, 1, 2}]