\[ \left \{x''(t)=\text {a1} x(t)+\text {b1} y(t)+\text {c1},y''(t)=\text {a2} x(t)+\text {b2} y(t)+\text {c2}\right \} \] ✓ Mathematica : cpu = 13.5511 (sec), leaf count = 17774 \[ \text {Too large to display} \] ✓ Maple : cpu = 0.256 (sec), leaf count = 457
\[\left \{\left \{x \left (t \right ) = c_{1} {\mathrm e}^{-\frac {\sqrt {2 \mathit {a1} +2 \mathit {b2} -2 \sqrt {\mathit {a1}^{2}-2 \mathit {a1} \mathit {b2} +4 \mathit {a2} \mathit {b1} +\mathit {b2}^{2}}}\, 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 {a2} \mathit {b1} +\mathit {b2}^{2}}}\, t}{2}}+c_{3} {\mathrm e}^{-\frac {\sqrt {2 \mathit {a1} +2 \mathit {b2} +2 \sqrt {\mathit {a1}^{2}-2 \mathit {a1} \mathit {b2} +4 \mathit {a2} \mathit {b1} +\mathit {b2}^{2}}}\, t}{2}}+c_{4} {\mathrm e}^{\frac {\sqrt {2 \mathit {a1} +2 \mathit {b2} +2 \sqrt {\mathit {a1}^{2}-2 \mathit {a1} \mathit {b2} +4 \mathit {a2} \mathit {b1} +\mathit {b2}^{2}}}\, t}{2}}+\frac {\mathit {b1} \mathit {c2}}{\mathit {a1} \mathit {b2} -\mathit {a2} \mathit {b1}}-\frac {\mathit {b2} \mathit {c1}}{\mathit {a1} \mathit {b2} -\mathit {a2} \mathit {b1}}, y \left (t \right ) = \frac {-c_{1} \left (\mathit {a1} \mathit {b2} -\mathit {a2} \mathit {b1} \right ) \left (\mathit {a1} -\mathit {b2} +\sqrt {\mathit {a1}^{2}-2 \mathit {a1} \mathit {b2} +4 \mathit {a2} \mathit {b1} +\mathit {b2}^{2}}\right ) {\mathrm e}^{-\frac {\sqrt {2 \mathit {a1} +2 \mathit {b2} -2 \sqrt {\mathit {a1}^{2}-2 \mathit {a1} \mathit {b2} +4 \mathit {a2} \mathit {b1} +\mathit {b2}^{2}}}\, t}{2}}-c_{2} \left (\mathit {a1} \mathit {b2} -\mathit {a2} \mathit {b1} \right ) \left (\mathit {a1} -\mathit {b2} +\sqrt {\mathit {a1}^{2}-2 \mathit {a1} \mathit {b2} +4 \mathit {a2} \mathit {b1} +\mathit {b2}^{2}}\right ) {\mathrm e}^{\frac {\sqrt {2 \mathit {a1} +2 \mathit {b2} -2 \sqrt {\mathit {a1}^{2}-2 \mathit {a1} \mathit {b2} +4 \mathit {a2} \mathit {b1} +\mathit {b2}^{2}}}\, t}{2}}+c_{3} \left (\mathit {a1} \mathit {b2} -\mathit {a2} \mathit {b1} \right ) \left (-\mathit {a1} +\mathit {b2} +\sqrt {\mathit {a1}^{2}-2 \mathit {a1} \mathit {b2} +4 \mathit {a2} \mathit {b1} +\mathit {b2}^{2}}\right ) {\mathrm e}^{-\frac {\sqrt {2 \mathit {a1} +2 \mathit {b2} +2 \sqrt {\mathit {a1}^{2}-2 \mathit {a1} \mathit {b2} +4 \mathit {a2} \mathit {b1} +\mathit {b2}^{2}}}\, t}{2}}+c_{4} \left (\mathit {a1} \mathit {b2} -\mathit {a2} \mathit {b1} \right ) \left (-\mathit {a1} +\mathit {b2} +\sqrt {\mathit {a1}^{2}-2 \mathit {a1} \mathit {b2} +4 \mathit {a2} \mathit {b1} +\mathit {b2}^{2}}\right ) {\mathrm e}^{\frac {\sqrt {2 \mathit {a1} +2 \mathit {b2} +2 \sqrt {\mathit {a1}^{2}-2 \mathit {a1} \mathit {b2} +4 \mathit {a2} \mathit {b1} +\mathit {b2}^{2}}}\, t}{2}}-2 \left (\mathit {a1} \mathit {c2} -\mathit {a2} \mathit {c1} \right ) \mathit {b1}}{2 \left (\mathit {a1} \mathit {b2} -\mathit {a2} \mathit {b1} \right ) \mathit {b1}}\right \}\right \}\]