#
# Numerical Mathematics and Computing, Fifth Edition
# Ward Cheney & David Kincaid
# Brooks/Cole Publ. Co.
# (c) 2003
#
# file:  ode_sys1
#
# Solving system of ODE:
# x'(t) = x(t) - y(t) + 2t - t^2 - t^3
# y'(t) = x(t) + y(t) - 4t^2 + t^3
# with initial conditions:  x(0)=1, y(0)=0

# For analytic solution:

 sysode := {D(x)(t) = x(t) - y(t) +2*t -t^2 - t^3,
            D(y)(t) = x(t) + y(t) -4*t^2 + t^3};
 fcns := {x(t), y(t)};
 ic := {x(0) = 1, y(0) = 0};
 f  := dsolve(sysode union ic, fcns);

# Alternative numerical solution:

 f := dsolve( sysode union ic, fcns, numeric);
 f(0);
 f(1);