ODE No. 1883

10.28 ODE No. 1883

${\frac{d}{d t} x (t) - \frac{d}{d t} y (t) + x (t) = 2 t, \frac{d^{2}}{d t^{2}} x (t) + \frac{d}{d t} y (t) - 9 x (t) + 3 y (t) = \sin (2 t)}$

Mathematica: cpu = 0.590075 (sec), leaf count = 614 ${{x (t) \to \frac{1}{16} c_{1} e^{- 3 t} (20 e^{4 t} t + 7 e^{4 t} + 9) + \frac{1}{16} c_{2} e^{- 3 t} (4 e^{4 t} t + 3 e^{4 t} - 3) - \frac{3}{16} c_{3} e^{- 3 t} (4 e^{4 t} t - e^{4 t} + 1) + \frac{e^{- 4 t} (20 e^{4 t} t + 7 e^{4 t} + 9) (10400 (t^{2} + 2 t + 2) + (260 t - 225 e^{4 t} - 351) \sin (2 t) + 2 (260 t + 75 e^{4 t} - 91) \cos (2 t))}{83200} - \frac{3 e^{- 4 t} (4 e^{4 t} t - e^{4 t} + 1) (5200 (2 t^{2} + 5 t + 5) + (260 t - 75 e^{4 t} - 221) \sin (2 t) + (520 t + 50 e^{4 t} + 78) \cos (2 t))}{41600} + \frac{e^{- 4 t} (4 e^{4 t} t + 3 e^{4 t} - 3) (130 (40 (t^{2} + t + 1) + t \sin (2 t)) + (260 t - 225 e^{4 t} - 351) \cos (2 t) + (675 e^{4 t} - 611) \sin (t) \cos (t))}{41600}, y (t) \to \frac{1}{8} c_{1} e^{- 3 t} (20 e^{4 t} t - 3 e^{4 t} + 3) + \frac{1}{8} c_{2} e^{- 3 t} (4 e^{4 t} t + e^{4 t} - 1) - \frac{1}{8} c_{3} e^{- 3 t} (12 e^{4 t} t - 9 e^{4 t} + 1) + \frac{e^{- 4 t} (20 e^{4 t} t - 3 e^{4 t} + 3) (10400 (t^{2} + 2 t + 2) + (260 t - 225 e^{4 t} - 351) \sin (2 t) + 2 (260 t + 75 e^{4 t} - 91) \cos (2 t))}{41600} - \frac{e^{- 4 t} (12 e^{4 t} t - 9 e^{4 t} + 1) (5200 (2 t^{2} + 5 t + 5) + (260 t - 75 e^{4 t} - 221) \sin (2 t) + (520 t + 50 e^{4 t} + 78) \cos (2 t))}{20800} + \frac{e^{- 4 t} (4 e^{4 t} t + e^{4 t} - 1) (130 (40 (t^{2} + t + 1) + t \sin (2 t)) + (260 t - 225 e^{4 t} - 351) \cos (2 t) + (675 e^{4 t} - 611) \sin (t) \cos (t))}{20800}}}$

Maple: cpu = 0.094 (sec), leaf count = 80 ${{x (t) = - \frac{2 \cos (2 t)}{325} + 4 - \frac{36 \sin (2 t)}{325} + 2 t +_C 1 e^{t} +_C 2 e^{- 3 t} +_C 3 e^{t} t, y (t) = \frac{16 \cos (2 t)}{325} - \frac{37 \sin (2 t)}{325} + 2_C 1 e^{t} + \frac{2_C 2 e^{- 3 t}}{3} + 2_C 3 e^{t} t -_C 3 e^{t} + 10 + 6 t}}$

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