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 = 13.5511 (sec), leaf count = 17774 $Too large to display$ ✓ Maple : cpu = 0.256 (sec), leaf count = 457

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

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