\[ \boxed { \left \{ {\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}x \left ( t \right ) ={\it a1}\,x \left ( t \right ) +{\it b1}\,y \left ( t \right ) +{\it c1},{\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}y \left ( t \right ) ={\it a2}\,x \left ( t \right ) +{\it b2}\,y \left ( t \right ) +{\it c2} \right \} } \]
Mathematica: cpu = 25.510739 (sec), leaf count = 37858 \[ \text {Unable to display Latex} \]
Maple: cpu = 0.171 (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\,\sqrt {{{\it a1}}^{2 }-2\,{\it a1}\,{\it b2}+4\,{\it a2}\,{\it b1}+{{\it b2}}^{2}}+2\,{\it a1}+2\,{\it b2}}}}}+{\it \_C1}\,{{\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}\,{\it b1}}{ {\it a1}\,{\it b2}-{\it a2}\,{\it b1}}}-{\frac {{\it b2}\,{\it c1}}{{ \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\,\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 \_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\,\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 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 \} \]