(*						      *)
(* Numerical Mathematics and Computing, Fifth Edition *)
(* Ward Cheney & David Kincaid		              *)
(* Brooks/Cole Publ. Co.			      *)
(* (c) 2004                                           *)
(* 				.	              *)
(* File: ode_sys1 				      *)

(* solution of uncoupled system of ODEs *)
DSolve[{x'[t] == x[t] - y[t] + 2*t - t^2 - t^3, 
         y'[t] == x[t] + y[t] - 4*t^2 + t^3, 
        x[0] == 1, y[0] == 0}, {x[t], y[t]}, t ]

(* solution of system of ODEs *)
NDSolve[{x'[t] == x[t] - y[t] +t*(2 - t*(1 + t)),
         y'[t] == x[t] + y[t] - t*t*(4 - t), 
         x[0] == 1, y[0] == 0}, {x, y}, {t, 0, 1}]
x[1] /. %
y[1] /. %%