\[ \left \{x''(t)=\text {a1} x(t)+\text {b1} y(t)+\text {c1},y''(t)=\text {a2} x(t)+\text {b2} y(t)+\text {c2}\right \} \] ✓ Mathematica : cpu = 24.0837 (sec), leaf count = 37858
\[\text {Too large to display}\]
✓ Maple : cpu = 0.224 (sec), leaf count = 634
\[ \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 b1}\,{\it c2}}{{\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 {{\it \_C4}}{2\,{\it b1}\, \left ( {\it a1}\,{\it b2}-{\it a2}\,{\it b1} \right ) } \left ( -{\it a1}\,{{\it b2}}^{2}+ \left ( -\sqrt {{{\it a1}}^{2}-2\,{\it a1}\,{\it b2}+4\,{\it a2}\,{\it b1}+{{\it b2}}^{2}}{\it a1}+{{\it a1}}^{2}+{\it a2}\,{\it b1} \right ) {\it b2}+ \left ( \sqrt {{{\it a1}}^{2}-2\,{\it a1}\,{\it b2}+4\,{\it a2}\,{\it b1}+{{\it b2}}^{2}}-{\it a1} \right ) {\it a2}\,{\it b1} \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}}}}}}-{\frac {{\it \_C3}}{2\,{\it b1}\, \left ( {\it a1}\,{\it b2}-{\it a2}\,{\it b1} \right ) } \left ( -{\it a1}\,{{\it b2}}^{2}+ \left ( -\sqrt {{{\it a1}}^{2}-2\,{\it a1}\,{\it b2}+4\,{\it a2}\,{\it b1}+{{\it b2}}^{2}}{\it a1}+{{\it a1}}^{2}+{\it a2}\,{\it b1} \right ) {\it b2}+ \left ( \sqrt {{{\it a1}}^{2}-2\,{\it a1}\,{\it b2}+4\,{\it a2}\,{\it b1}+{{\it b2}}^{2}}-{\it a1} \right ) {\it a2}\,{\it b1} \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}}}}}}-{\frac {{\it \_C2}}{2\,{\it b1}\, \left ( {\it a1}\,{\it b2}-{\it a2}\,{\it b1} \right ) } \left ( -{\it a1}\,{{\it b2}}^{2}+ \left ( \sqrt {{{\it a1}}^{2}-2\,{\it a1}\,{\it b2}+4\,{\it a2}\,{\it b1}+{{\it b2}}^{2}}{\it a1}+{{\it a1}}^{2}+{\it a2}\,{\it b1} \right ) {\it b2}+ \left ( -\sqrt {{{\it a1}}^{2}-2\,{\it a1}\,{\it b2}+4\,{\it a2}\,{\it b1}+{{\it b2}}^{2}}-{\it a1} \right ) {\it a2}\,{\it b1} \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}}}}}}}-{\frac {{\it \_C1}}{2\,{\it b1}\, \left ( {\it a1}\,{\it b2}-{\it a2}\,{\it b1} \right ) } \left ( -{\it a1}\,{{\it b2}}^{2}+ \left ( \sqrt {{{\it a1}}^{2}-2\,{\it a1}\,{\it b2}+4\,{\it a2}\,{\it b1}+{{\it b2}}^{2}}{\it a1}+{{\it a1}}^{2}+{\it a2}\,{\it b1} \right ) {\it b2}+ \left ( -\sqrt {{{\it a1}}^{2}-2\,{\it a1}\,{\it b2}+4\,{\it a2}\,{\it b1}+{{\it b2}}^{2}}-{\it a1} \right ) {\it a2}\,{\it b1} \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}}}}}}}-{\frac {{\it a1}\,{\it c2}}{{\it a1}\,{\it b2}-{\it a2}\,{\it b1}}}+{\frac {{\it a2}\,{\it c1}}{{\it a1}\,{\it b2}-{\it a2}\,{\it b1}}} \right \} \right \} \]