ODE No. 1888

10.33 ODE No. 1888

${\frac{d^{2}}{d t^{2}} x (t) = a 1 x (t) + b 1 y (t) + c 1, \frac{d^{2}}{d t^{2}} y (t) = a 2 x (t) + b 2 y (t) + c 2}$

Mathematica: cpu = 25.510739 (sec), leaf count = 37858 $Unable to display Latex$

Maple: cpu = 0.171 (sec), leaf count = 634 ${{x (t) =_C 4 e^{\frac{t}{2} \sqrt{2 \sqrt{{a 1}^{2} - 2 a 1 b 2 + 4 a 2 b 1 + {b 2}^{2}} + 2 a 1 + 2 b 2}} +_C 3 e^{- \frac{t}{2} \sqrt{2 \sqrt{{a 1}^{2} - 2 a 1 b 2 + 4 a 2 b 1 + {b 2}^{2}} + 2 a 1 + 2 b 2}} +_C 2 e^{\frac{t}{2} \sqrt{- 2 \sqrt{{a 1}^{2} - 2 a 1 b 2 + 4 a 2 b 1 + {b 2}^{2}} + 2 a 1 + 2 b 2}} +_C 1 e^{- \frac{t}{2} \sqrt{- 2 \sqrt{{a 1}^{2} - 2 a 1 b 2 + 4 a 2 b 1 + {b 2}^{2}} + 2 a 1 + 2 b 2}} + \frac{c 2 b 1}{a 1 b 2 - a 2 b 1} - \frac{b 2 c 1}{a 1 b 2 - a 2 b 1}, y (t) = \frac{_C 4}{2 b 1 (a 1 b 2 - a 2 b 1)} (a 1 {b 2}^{2} + (\sqrt{{a 1}^{2} - 2 a 1 b 2 + 4 a 2 b 1 + {b 2}^{2}} a 1 - {a 1}^{2} - a 2 b 1) b 2 + (- \sqrt{{a 1}^{2} - 2 a 1 b 2 + 4 a 2 b 1 + {b 2}^{2}} + a 1) a 2 b 1) e^{\frac{t}{2} \sqrt{2 \sqrt{{a 1}^{2} - 2 a 1 b 2 + 4 a 2 b 1 + {b 2}^{2}} + 2 a 1 + 2 b 2}} + \frac{_C 3}{2 b 1 (a 1 b 2 - a 2 b 1)} (a 1 {b 2}^{2} + (\sqrt{{a 1}^{2} - 2 a 1 b 2 + 4 a 2 b 1 + {b 2}^{2}} a 1 - {a 1}^{2} - a 2 b 1) b 2 + (- \sqrt{{a 1}^{2} - 2 a 1 b 2 + 4 a 2 b 1 + {b 2}^{2}} + a 1) a 2 b 1) e^{- \frac{t}{2} \sqrt{2 \sqrt{{a 1}^{2} - 2 a 1 b 2 + 4 a 2 b 1 + {b 2}^{2}} + 2 a 1 + 2 b 2}} + \frac{_C 2}{2 b 1 (a 1 b 2 - a 2 b 1)} (a 1 {b 2}^{2} + (- \sqrt{{a 1}^{2} - 2 a 1 b 2 + 4 a 2 b 1 + {b 2}^{2}} a 1 - {a 1}^{2} - a 2 b 1) b 2 + (\sqrt{{a 1}^{2} - 2 a 1 b 2 + 4 a 2 b 1 + {b 2}^{2}} + a 1) a 2 b 1) e^{\frac{t}{2} \sqrt{- 2 \sqrt{{a 1}^{2} - 2 a 1 b 2 + 4 a 2 b 1 + {b 2}^{2}} + 2 a 1 + 2 b 2}} + \frac{_C 1}{2 b 1 (a 1 b 2 - a 2 b 1)} (a 1 {b 2}^{2} + (- \sqrt{{a 1}^{2} - 2 a 1 b 2 + 4 a 2 b 1 + {b 2}^{2}} a 1 - {a 1}^{2} - a 2 b 1) b 2 + (\sqrt{{a 1}^{2} - 2 a 1 b 2 + 4 a 2 b 1 + {b 2}^{2}} + a 1) a 2 b 1) e^{- \frac{t}{2} \sqrt{- 2 \sqrt{{a 1}^{2} - 2 a 1 b 2 + 4 a 2 b 1 + {b 2}^{2}} + 2 a 1 + 2 b 2}} - \frac{a 1 c 2}{a 1 b 2 - a 2 b 1} + \frac{a 2 c 1}{a 1 b 2 - a 2 b 1}}}$

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