ODE No. 1888

2.1888 ODE No. 1888

${x^{″} (t) = a1 x (t) + b1 y (t) + c1, y^{″} (t) = a2 x (t) + b2 y (t) + c2}$ ✓ Mathematica : cpu = 24.0837 (sec), leaf count = 37858

$Too large to display$

✓ Maple : cpu = 0.224 (sec), leaf count = 634

${{x (t) =_C 4 e^{\frac{t}{2} \sqrt{2 \sqrt{{a 1}^{2} - 2 a 1 b 2 + 4 a 2 b 1 + {b 2}^{2}} + 2 a 1 + 2 b 2}} +_C 3 e^{- \frac{t}{2} \sqrt{2 \sqrt{{a 1}^{2} - 2 a 1 b 2 + 4 a 2 b 1 + {b 2}^{2}} + 2 a 1 + 2 b 2}} +_C 2 e^{\frac{t}{2} \sqrt{2 a 1 + 2 b 2 - 2 \sqrt{{a 1}^{2} - 2 a 1 b 2 + 4 a 2 b 1 + {b 2}^{2}}}} +_C 1 e^{- \frac{t}{2} \sqrt{2 a 1 + 2 b 2 - 2 \sqrt{{a 1}^{2} - 2 a 1 b 2 + 4 a 2 b 1 + {b 2}^{2}}}} + \frac{b 1 c 2}{a 1 b 2 - a 2 b 1} - \frac{c 1 b 2}{a 1 b 2 - a 2 b 1}, y (t) = - \frac{_C 4}{2 b 1 (a 1 b 2 - a 2 b 1)} (- a 1 {b 2}^{2} + (- \sqrt{{a 1}^{2} - 2 a 1 b 2 + 4 a 2 b 1 + {b 2}^{2}} a 1 + {a 1}^{2} + a 2 b 1) b 2 + (\sqrt{{a 1}^{2} - 2 a 1 b 2 + 4 a 2 b 1 + {b 2}^{2}} - a 1) a 2 b 1) e^{\frac{t}{2} \sqrt{2 \sqrt{{a 1}^{2} - 2 a 1 b 2 + 4 a 2 b 1 + {b 2}^{2}} + 2 a 1 + 2 b 2}} - \frac{_C 3}{2 b 1 (a 1 b 2 - a 2 b 1)} (- a 1 {b 2}^{2} + (- \sqrt{{a 1}^{2} - 2 a 1 b 2 + 4 a 2 b 1 + {b 2}^{2}} a 1 + {a 1}^{2} + a 2 b 1) b 2 + (\sqrt{{a 1}^{2} - 2 a 1 b 2 + 4 a 2 b 1 + {b 2}^{2}} - a 1) a 2 b 1) e^{- \frac{t}{2} \sqrt{2 \sqrt{{a 1}^{2} - 2 a 1 b 2 + 4 a 2 b 1 + {b 2}^{2}} + 2 a 1 + 2 b 2}} - \frac{_C 2}{2 b 1 (a 1 b 2 - a 2 b 1)} (- a 1 {b 2}^{2} + (\sqrt{{a 1}^{2} - 2 a 1 b 2 + 4 a 2 b 1 + {b 2}^{2}} a 1 + {a 1}^{2} + a 2 b 1) b 2 + (- \sqrt{{a 1}^{2} - 2 a 1 b 2 + 4 a 2 b 1 + {b 2}^{2}} - a 1) a 2 b 1) e^{\frac{t}{2} \sqrt{2 a 1 + 2 b 2 - 2 \sqrt{{a 1}^{2} - 2 a 1 b 2 + 4 a 2 b 1 + {b 2}^{2}}}} - \frac{_C 1}{2 b 1 (a 1 b 2 - a 2 b 1)} (- a 1 {b 2}^{2} + (\sqrt{{a 1}^{2} - 2 a 1 b 2 + 4 a 2 b 1 + {b 2}^{2}} a 1 + {a 1}^{2} + a 2 b 1) b 2 + (- \sqrt{{a 1}^{2} - 2 a 1 b 2 + 4 a 2 b 1 + {b 2}^{2}} - a 1) a 2 b 1) e^{- \frac{t}{2} \sqrt{2 a 1 + 2 b 2 - 2 \sqrt{{a 1}^{2} - 2 a 1 b 2 + 4 a 2 b 1 + {b 2}^{2}}}} - \frac{a 1 c 2}{a 1 b 2 - a 2 b 1} + \frac{a 2 c 1}{a 1 b 2 - a 2 b 1}}}$

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