ODE No. 1884

10.29 ODE No. 1884

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

Mathematica: cpu = 0.180523 (sec), leaf count = 226 ${{x (t) \to 7 (c_{2} + t^{2} - \frac{1}{2} \sin (2 t)) + 8 (c_{1} e^{t / 2} + c_{2} (e^{t / 2} - 1) + \frac{1}{68} e^{- t / 2} (e^{t / 2} \cos (2 t) - 2 (17 (2 e^{t / 2} t^{2} + e^{t / 2} (t + 2)) - 15 e^{t / 2} \sin (2 t)))), y (t) \to \frac{3}{2} (c_{2} + t^{2} - \frac{1}{2} \sin (2 t)) + 2 (c_{1} e^{t / 2} + c_{2} (e^{t / 2} - 1) + \frac{1}{68} e^{- t / 2} (e^{t / 2} \cos (2 t) - 2 (17 (2 e^{t / 2} t^{2} + e^{t / 2} (t + 2)) - 15 e^{t / 2} \sin (2 t))))}}$

Maple: cpu = 0.078 (sec), leaf count = 69 ${{x (t) = \frac{\sin (2 t)}{34} + \frac{2 \cos (2 t)}{17} - t^{2} + 2_C 1 e^{t / 2} - 4 t +_C 2, y (t) = \frac{\cos (2 t)}{34} + \frac{9 \sin (2 t)}{68} - t + \frac{_C 1}{2} e^{\frac{t}{2}} + 2 - \frac{t^{2}}{2} + \frac{_C 2}{2}}}$

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