ODE No. 1888

2.1888 ODE No. 1888

Problem in Latex
Mathematica input
Maple input

${x^{″} (t) = a1 x (t) + b1 y (t) + c1, y^{″} (t) = a2 x (t) + b2 y (t) + c2}$ ✓ Mathematica : cpu = 9.05439 (sec), leaf count = 15664 $Too large to display$ ✓ Maple : cpu = 0.315 (sec), leaf count = 457

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

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