ODE No. 1896

10.41 ODE No. 1896

${\frac{d^{3}}{d t^{3}} y (t) - \frac{d^{2}}{d t^{2}} y (t) + 2 \frac{d}{d t} x (t) - x (t) = t, \frac{d^{2}}{d t^{2}} x (t) - 2 \frac{d}{d t} x (t) - \frac{d}{d t} y (t) + y (t) = 0}$

Mathematica: cpu = 0.197525 (sec), leaf count = 1132 ${{x (t) \to \frac{1}{64} e^{- t} (2 e^{2 t} t^{2} - 6 e^{2 t} t + 7 e^{2 t} + 1) (e^{t} (1 - t) + e^{- t} (- 2 t^{3} - 8 t^{2} - 17 t - 17)) + \frac{1}{64} e^{- t} (2 e^{2 t} t^{2} + 6 e^{2 t} t + e^{2 t} - 1) (e^{t} (t - 1) + e^{- t} (- 2 t^{3} - 4 t^{2} - 7 t - 7)) - \frac{1}{384} e^{- t} (2 e^{2 t} t^{2} + 2 e^{2 t} t - e^{2 t} + 1) (e^{t} (9 t - 9) + e^{- t} (- 4 t^{4} - 22 t^{3} - 48 t^{2} - 87 t - 87)) + \frac{1}{384} e^{- t} (2 e^{2 t} t^{2} - 2 e^{2 t} t + e^{2 t} - 1) (e^{t} (9 t - 9) + e^{- t} (- 4 t^{4} + 2 t^{3} + 24 t^{2} + 9 t + 9)) + \frac{1}{192} e^{- t} (2 e^{2 t} t - e^{2 t} + 1) (- e^{t} (9 t - 9) - e^{- t} (4 t^{4} + 10 t^{3} + 9 t + 9)) + \frac{1}{8} e^{- t} (2 e^{2 t} t^{2} - 6 e^{2 t} t + 7 e^{2 t} + 1) c_{1} + \frac{1}{8} e^{- t} (2 e^{2 t} t^{2} + 6 e^{2 t} t + e^{2 t} - 1) c_{2} - \frac{1}{8} e^{- t} (2 e^{2 t} t^{2} + 2 e^{2 t} t - e^{2 t} + 1) c_{3} + \frac{1}{4} e^{- t} (2 e^{2 t} t - e^{2 t} + 1) c_{4} + \frac{1}{8} e^{- t} (2 e^{2 t} t^{2} - 2 e^{2 t} t + e^{2 t} - 1) c_{5}, y (t) \to - \frac{1}{384} e^{- t} (4 e^{2 t} t^{3} - 18 e^{2 t} t^{2} + 18 e^{2 t} t - 9 e^{2 t} + 9) (e^{t} (1 - t) + e^{- t} (- 2 t^{3} - 8 t^{2} - 17 t - 17)) - \frac{1}{384} e^{- t} (4 e^{2 t} t^{3} + 18 e^{2 t} t^{2} - 18 e^{2 t} t + 9 e^{2 t} - 9) (e^{t} (t - 1) + e^{- t} (- 2 t^{3} - 4 t^{2} - 7 t - 7)) + \frac{e^{- t} (4 e^{2 t} t^{3} + 6 e^{2 t} t^{2} - 30 e^{2 t} t + 39 e^{2 t} + 9) (e^{t} (9 t - 9) + e^{- t} (- 4 t^{4} - 22 t^{3} - 48 t^{2} - 87 t - 87))}{2304} - \frac{e^{- t} (4 e^{2 t} t^{3} - 6 e^{2 t} t^{2} - 18 e^{2 t} t + 9 e^{2 t} - 9) (e^{t} (9 t - 9) + e^{- t} (- 4 t^{4} + 2 t^{3} + 24 t^{2} + 9 t + 9))}{2304} - \frac{1}{384} e^{- t} (2 e^{2 t} t^{2} - 2 e^{2 t} t - 3 e^{2 t} + 3) (- e^{t} (9 t - 9) - e^{- t} (4 t^{4} + 10 t^{3} + 9 t + 9)) - \frac{1}{48} e^{- t} (4 e^{2 t} t^{3} - 18 e^{2 t} t^{2} + 18 e^{2 t} t - 9 e^{2 t} + 9) c_{1} - \frac{1}{48} e^{- t} (4 e^{2 t} t^{3} + 18 e^{2 t} t^{2} - 18 e^{2 t} t + 9 e^{2 t} - 9) c_{2} + \frac{1}{48} e^{- t} (4 e^{2 t} t^{3} + 6 e^{2 t} t^{2} - 30 e^{2 t} t + 39 e^{2 t} + 9) c_{3} - \frac{1}{8} e^{- t} (2 e^{2 t} t^{2} - 2 e^{2 t} t - 3 e^{2 t} + 3) c_{4} - \frac{1}{48} e^{- t} (4 e^{2 t} t^{3} - 6 e^{2 t} t^{2} - 18 e^{2 t} t + 9 e^{2 t} - 9) c_{5}}}$

Maple: cpu = 0.031 (sec), leaf count = 75 ${{x (t) = - 2 - t -_C 3 e^{t} - 6_C 5 e^{t} - \frac{2_C 2 e^{- t}}{3} - 2_C 4 e^{t} t - 3_C 5 e^{t} t^{2}, y (t) = - 2 +_C 1 e^{t} +_C 2 e^{- t} +_C 3 e^{t} t +_C 4 e^{t} t^{2} +_C 5 e^{t} t^{3}}}$

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