diff ( x1 , t , 1 ) = 4.0 * x2 - 2.0 * diff ( x2 , t , 1 ) - 2.0 * x1 ; diff ( x2 , t , 2 ) = 3.0 * diff ( x2 , t , 1 ) - 2.0 * x2 - diff ( x1 , t , 2) - diff ( x1 , t , 1 ) + x1 ; ! Digits := 64; max_terms:=30; ! # problem from Boyce DePrima - # _Elementary Differential Equations and Boundary Value Problems_ # page 269 # t_start := 0.5; t_end := 0.8; diff(x1,0,exact_soln_x1(t_start)); # I think following line should be omitted # diff(x1,1,exact_soln_x1p(t_start)); diff(x2,0,exact_soln_x2(t_start)); diff(x2,1,exact_soln_x2p(t_start)); glob_look_poles := true; glob_max_h := 0.0001; ! exact_soln_x1 := proc(t) local c1,c2,c3; c1 := 1.0; c2 := 0.0002; c3 := 0.0003; return(2.0 * c1 + 6.0 * c3 * exp(-t)); end; exact_soln_x1p := proc(t) local c1,c2,c3; c1 := 1.0; c2 := 0.0002; c3 := 0.0003; return( - 6.0 * c3 * exp(-t)); end; exact_soln_x2 := proc(t) local c1,c2,c3; c1 := 1.0; c2 := 0.0002; c3 := 0.0003; return(c1 + c2 * exp(2.0 * t) + c3 * exp(-t)); end; exact_soln_x2p := proc(t) local c1,c2,c3; c1 := 1.0; c2 := 0.0002; c3 := 0.0003; return( 2.0 * c2 * exp(2.0 * t) - c3 * exp(-t)); end;