\[ \left \{x''(t)=\text {a1} x(t)+\text {b1} y(t)+\text {c1},y''(t)=\text {a2} x(t)+\text {b2} y(t)+\text {c2}\right \} \] ✓ Mathematica : cpu = 27.0799 (sec), leaf count = 20302
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✓ Maple : cpu = 0.24 (sec), leaf count = 457
\[ \left \{ \left \{ x \left ( t \right ) ={\it \_C4}\,{{\rm e}^{{\frac {t}{2}\sqrt {2\,\sqrt {{{\it a1}}^{2}-2\,{\it a1}\,{\it b2}+4\,{\it a2}\,{\it b1}+{{\it b2}}^{2}}+2\,{\it a1}+2\,{\it b2}}}}}+{\it \_C3}\,{{\rm e}^{-{\frac {t}{2}\sqrt {2\,\sqrt {{{\it a1}}^{2}-2\,{\it a1}\,{\it b2}+4\,{\it a2}\,{\it b1}+{{\it b2}}^{2}}+2\,{\it a1}+2\,{\it b2}}}}}+{\it \_C2}\,{{\rm e}^{{\frac {t}{2}\sqrt {2\,{\it a1}+2\,{\it b2}-2\,\sqrt {{{\it a1}}^{2}-2\,{\it a1}\,{\it b2}+4\,{\it a2}\,{\it b1}+{{\it b2}}^{2}}}}}}+{\it \_C1}\,{{\rm e}^{-{\frac {t}{2}\sqrt {2\,{\it a1}+2\,{\it b2}-2\,\sqrt {{{\it a1}}^{2}-2\,{\it a1}\,{\it b2}+4\,{\it a2}\,{\it b1}+{{\it b2}}^{2}}}}}}+{\frac {{\it c2}\,{\it b1}}{{\it a1}\,{\it b2}-{\it a2}\,{\it b1}}}-{\frac {{\it c1}\,{\it b2}}{{\it a1}\,{\it b2}-{\it a2}\,{\it b1}}},y \left ( t \right ) ={\frac {1}{2\,{\it b1}\, \left ( {\it a1}\,{\it b2}-{\it a2}\,{\it b1} \right ) } \left ( -{\it \_C1}\, \left ( {\it a1}\,{\it b2}-{\it a2}\,{\it b1} \right ) \left ( \sqrt {{{\it a1}}^{2}-2\,{\it a1}\,{\it b2}+4\,{\it a2}\,{\it b1}+{{\it b2}}^{2}}+{\it a1}-{\it b2} \right ) {{\rm e}^{-{\frac {t}{2}\sqrt {2\,{\it a1}+2\,{\it b2}-2\,\sqrt {{{\it a1}}^{2}-2\,{\it a1}\,{\it b2}+4\,{\it a2}\,{\it b1}+{{\it b2}}^{2}}}}}}-{\it \_C2}\, \left ( {\it a1}\,{\it b2}-{\it a2}\,{\it b1} \right ) \left ( \sqrt {{{\it a1}}^{2}-2\,{\it a1}\,{\it b2}+4\,{\it a2}\,{\it b1}+{{\it b2}}^{2}}+{\it a1}-{\it b2} \right ) {{\rm e}^{{\frac {t}{2}\sqrt {2\,{\it a1}+2\,{\it b2}-2\,\sqrt {{{\it a1}}^{2}-2\,{\it a1}\,{\it b2}+4\,{\it a2}\,{\it b1}+{{\it b2}}^{2}}}}}}+{\it \_C3}\, \left ( {\it a1}\,{\it b2}-{\it a2}\,{\it b1} \right ) \left ( \sqrt {{{\it a1}}^{2}-2\,{\it a1}\,{\it b2}+4\,{\it a2}\,{\it b1}+{{\it b2}}^{2}}-{\it a1}+{\it b2} \right ) {{\rm e}^{-{\frac {t}{2}\sqrt {2\,\sqrt {{{\it a1}}^{2}-2\,{\it a1}\,{\it b2}+4\,{\it a2}\,{\it b1}+{{\it b2}}^{2}}+2\,{\it a1}+2\,{\it b2}}}}}+{\it \_C4}\, \left ( {\it a1}\,{\it b2}-{\it a2}\,{\it b1} \right ) \left ( \sqrt {{{\it a1}}^{2}-2\,{\it a1}\,{\it b2}+4\,{\it a2}\,{\it b1}+{{\it b2}}^{2}}-{\it a1}+{\it b2} \right ) {{\rm e}^{{\frac {t}{2}\sqrt {2\,\sqrt {{{\it a1}}^{2}-2\,{\it a1}\,{\it b2}+4\,{\it a2}\,{\it b1}+{{\it b2}}^{2}}+2\,{\it a1}+2\,{\it b2}}}}}-2\,{\it b1}\, \left ( {\it a1}\,{\it c2}-{\it a2}\,{\it c1} \right ) \right ) } \right \} \right \} \]