#
# Numerical Mathematics and Computing, Fifth Edition
# Ward Cheney & David Kincaid
# Brooks/Cole Publ. Co.
# (c) 2003
#
# file:  bvp
#
# Solving two boudary-value problems:
# 1. x"(t)=exp(t)-3sin(t)+x'(t)-x(t)
#    with the boundary conditions  x(1)=1.09737491 and x'(1)=0
# 2. y"(t)=exp(t)-3sin(t)+y'(t)-y(t)
#    with the boundary conditions  y(1)=1.09737491 and y'(1)=1
# The solution is also evaluated at t = 1, 1.5, and 2.
# Be patient, Maple does not produce the solution instantaneously,
# (takes 20-30 minutes.)

 ode1 := (D@@2)(x)(t)=exp(t)-3*sin(t)+D(x)(t)-x(t);
 init1 := x(1)=1.09737491,D(x)(1)=0;
 xsol := dsolve({ode1,init1},x(t));
 x2 := rhs(evalf(subs(t=2,xsol)));
 ode2 := (D@@2)(y)(t)=exp(t)-3*sin(t)+D(y)(t)-y(t);
 init2 := y(1)=1.09737491,D(y)(1)=1;
 ysol := dsolve({ode2, init2}, y(t));
 y2 := rhs(evalf(subs(t=2,ysol)));
 p := (8.63749661-y2)/(x2-y2);
 sol := p*xsol+(1-p)*ysol;
 evalf(subs(t=1,sol));
 evalf(subs(t=2,sol));
 evalf(subs(t=1.5,sol));

# Maple is also able to solve this boundary value problem directly:

 ode := (D@@2)(x)(t)=exp(t)-3*sin(t)+D(x)(t)-x(t);
 cond := x(1)=1.09737491, x(2)=8.63749661;
 xsol := dsolve({ode, cond},x(t));