\[ \left \{-x'(t)+x''(t)+y'(t)=0,x''(t)-x(t)+y''(t)=0\right \} \] ✓ Mathematica : cpu = 0.0248989 (sec), leaf count = 420
\[\left \{\left \{x(t)\to -\frac {1}{5} c_1 e^{\frac {t}{2}-\frac {\sqrt {5} t}{2}} \left (\sqrt {5} e^{\sqrt {5} t}-5 e^{\frac {\sqrt {5} t}{2}+\frac {t}{2}}-\sqrt {5}\right )+\frac {c_2 e^{\frac {t}{2}-\frac {\sqrt {5} t}{2}} \left (e^{\sqrt {5} t}-1\right )}{\sqrt {5}}-\frac {1}{10} c_4 e^{\frac {t}{2}-\frac {\sqrt {5} t}{2}} \left (5 e^{\sqrt {5} t}+\sqrt {5} e^{\sqrt {5} t}-10 e^{\frac {\sqrt {5} t}{2}+\frac {t}{2}}+5-\sqrt {5}\right ),y(t)\to -\frac {1}{10} c_1 e^{-\frac {\sqrt {5} t}{2}} \left (-5 e^{t/2}-\sqrt {5} e^{t/2}+10 e^{\frac {\sqrt {5} t}{2}}-5 e^{\sqrt {5} t+\frac {t}{2}}+\sqrt {5} e^{\sqrt {5} t+\frac {t}{2}}\right )+\frac {1}{10} c_2 e^{-\frac {\sqrt {5} t}{2}} \left (-5 e^{t/2}-\sqrt {5} e^{t/2}+10 e^{\frac {\sqrt {5} t}{2}}-5 e^{\sqrt {5} t+\frac {t}{2}}+\sqrt {5} e^{\sqrt {5} t+\frac {t}{2}}\right )+\frac {c_4 e^{\frac {t}{2}-\frac {\sqrt {5} t}{2}} \left (e^{\sqrt {5} t}-1\right )}{\sqrt {5}}+c_3\right \}\right \}\] ✓ Maple : cpu = 0.195 (sec), leaf count = 71
\[ \left \{ \left \{ x \left ( t \right ) ={\frac {{\it \_C4}\, \left ( \sqrt {5}-1 \right ) }{2}{{\rm e}^{-{\frac { \left ( \sqrt {5}-1 \right ) t}{2}}}}}-{\frac {{\it \_C3}\, \left ( \sqrt {5}+1 \right ) }{2}{{\rm e}^{{\frac { \left ( \sqrt {5}+1 \right ) t}{2}}}}}+{\it \_C1}\,{{\rm e}^{t}},y \left ( t \right ) ={\it \_C2}+{\it \_C3}\,{{\rm e}^{{\frac { \left ( \sqrt {5}+1 \right ) t}{2}}}}+{\it \_C4}\,{{\rm e}^{-{\frac { \left ( \sqrt {5}-1 \right ) t}{2}}}} \right \} \right \} \]