(*						      *)
(* Numerical Mathematics and Computing, Fifth Edition *)
(* Ward Cheney & David Kincaid		              *)
(* Brooks/Cole Publ. Co.			      *)
(* (c) 2004                                           *)
(* No warranties implied or expressed.	              *)
(* File: ode_sys2 				      *)

(* solution system of first-order ODEs *)
NDSolve[{x'[t] == -(8/3)*x[t] - (4/3)*y[t] + z[t] + 12, 
         y'[t] == -(17/3)*x[t] - (4/3)*y[t] + z[t] + 29, 
         z'[t] == -(35/3)*x[t] + (14/3)*y[t] - 2*z[t] + 48, 
         x[0] == 0, y[0] == 0, z[0] == 0}, 
        {x, y, z}, {t, 0, 2.5}]
x[2.5] /. %
y[2.5] /. %%
z[2.5] /. %%%

(* version 2 *)
DSolve[{x'[t] == -(8/3)*x[t] - (4/3)*y[t] + z[t] + 12, 
        y'[t] == -(17/3)*x[t] - (4/3)*y[t] + z[t] + 29, 
        z'[t] == -(35/3)*x[t] + (14/3)*y[t] - 2*z[t] + 48, 
        x[0] == 0, y[0] == 0, z[0] == 0}, {x[t], y[t], z[t]}, t]


(* version 3 *)
MatrixForm[m = {{-8/3, -4/3, 1},
                {-17/3, -4/3, 1},
                {-35/3, 14/3, -2}}}
b = {12, 29, 48}
x[t] = Table[x[i][t], {i,1,3}]
eqns = Table[x[i]'[t] == m[[i]].x[t] + b[[i]], {i,1,3}]
init = Table[x[i][0] == 0, {i,1,3}]
sysm = Join[eqns, init]
DSolve[sysm, x[t], t]