\[ \left \{x''(t)=\text {a1} x(t)+\text {b1} y(t)+\text {c1},y''(t)=\text {a2} x(t)+\text {b2} y(t)+\text {c2}\right \} \] ✓ Mathematica : cpu = 8.4505 (sec), leaf count = 15664
DSolve[{Derivative[2][x][t] == c1 + a1*x[t] + b1*y[t], Derivative[2][y][t] == c2 + a2*x[t] + b2*y[t]},{x[t], y[t]},t]
\[ \text {Too large to display} \] ✓ Maple : cpu = 0.186 (sec), leaf count = 457
dsolve({diff(diff(x(t),t),t) = a1*x(t)+b1*y(t)+c1, diff(diff(y(t),t),t) = a2*x(t)+b2*y(t)+c2})
\[\left \{x \left (t \right ) = c_{4} {\mathrm e}^{\frac {\sqrt {2 \sqrt {\mathit {a1}^{2}-2 \mathit {a1} \mathit {b2} +4 \mathit {b1} \mathit {a2} +\mathit {b2}^{2}}+2 \mathit {a1} +2 \mathit {b2}}\, t}{2}}+c_{3} {\mathrm e}^{-\frac {\sqrt {2 \sqrt {\mathit {a1}^{2}-2 \mathit {a1} \mathit {b2} +4 \mathit {b1} \mathit {a2} +\mathit {b2}^{2}}+2 \mathit {a1} +2 \mathit {b2}}\, t}{2}}+c_{2} {\mathrm e}^{\frac {\sqrt {2 \mathit {a1} +2 \mathit {b2} -2 \sqrt {\mathit {a1}^{2}-2 \mathit {a1} \mathit {b2} +4 \mathit {b1} \mathit {a2} +\mathit {b2}^{2}}}\, t}{2}}+c_{1} {\mathrm e}^{-\frac {\sqrt {2 \mathit {a1} +2 \mathit {b2} -2 \sqrt {\mathit {a1}^{2}-2 \mathit {a1} \mathit {b2} +4 \mathit {b1} \mathit {a2} +\mathit {b2}^{2}}}\, t}{2}}+\frac {\mathit {c2} \mathit {b1}}{\mathit {a1} \mathit {b2} -\mathit {b1} \mathit {a2}}-\frac {\mathit {b2} \mathit {c1}}{\mathit {a1} \mathit {b2} -\mathit {b1} \mathit {a2}}, y \left (t \right ) = \frac {-c_{1} \left (\mathit {a1} \mathit {b2} -\mathit {b1} \mathit {a2} \right ) \left (\sqrt {\mathit {a1}^{2}-2 \mathit {a1} \mathit {b2} +4 \mathit {b1} \mathit {a2} +\mathit {b2}^{2}}+\mathit {a1} -\mathit {b2} \right ) {\mathrm e}^{-\frac {\sqrt {2 \mathit {a1} +2 \mathit {b2} -2 \sqrt {\mathit {a1}^{2}-2 \mathit {a1} \mathit {b2} +4 \mathit {b1} \mathit {a2} +\mathit {b2}^{2}}}\, t}{2}}-c_{2} \left (\mathit {a1} \mathit {b2} -\mathit {b1} \mathit {a2} \right ) \left (\sqrt {\mathit {a1}^{2}-2 \mathit {a1} \mathit {b2} +4 \mathit {b1} \mathit {a2} +\mathit {b2}^{2}}+\mathit {a1} -\mathit {b2} \right ) {\mathrm e}^{\frac {\sqrt {2 \mathit {a1} +2 \mathit {b2} -2 \sqrt {\mathit {a1}^{2}-2 \mathit {a1} \mathit {b2} +4 \mathit {b1} \mathit {a2} +\mathit {b2}^{2}}}\, t}{2}}+c_{3} \left (\mathit {a1} \mathit {b2} -\mathit {b1} \mathit {a2} \right ) \left (\sqrt {\mathit {a1}^{2}-2 \mathit {a1} \mathit {b2} +4 \mathit {b1} \mathit {a2} +\mathit {b2}^{2}}-\mathit {a1} +\mathit {b2} \right ) {\mathrm e}^{-\frac {\sqrt {2 \sqrt {\mathit {a1}^{2}-2 \mathit {a1} \mathit {b2} +4 \mathit {b1} \mathit {a2} +\mathit {b2}^{2}}+2 \mathit {a1} +2 \mathit {b2}}\, t}{2}}+c_{4} \left (\mathit {a1} \mathit {b2} -\mathit {b1} \mathit {a2} \right ) \left (\sqrt {\mathit {a1}^{2}-2 \mathit {a1} \mathit {b2} +4 \mathit {b1} \mathit {a2} +\mathit {b2}^{2}}-\mathit {a1} +\mathit {b2} \right ) {\mathrm e}^{\frac {\sqrt {2 \sqrt {\mathit {a1}^{2}-2 \mathit {a1} \mathit {b2} +4 \mathit {b1} \mathit {a2} +\mathit {b2}^{2}}+2 \mathit {a1} +2 \mathit {b2}}\, t}{2}}-2 \mathit {b1} \left (\mathit {a1} \mathit {c2} -\mathit {a2} \mathit {c1} \right )}{2 \mathit {b1} \left (\mathit {a1} \mathit {b2} -\mathit {b1} \mathit {a2} \right )}\right \}\]