\[ \left \{x''(t)-x'(t)+y'(t)=0,x''(t)-x(t)+y''(t)=0\right \} \] ✓ Mathematica : cpu = 0.0396588 (sec), leaf count = 246
\[\left \{\left \{x(t)\to -\frac {1}{10} e^{\frac {1}{2} \left (t-\sqrt {5} t\right )} \left (2 c_1 \left (\sqrt {5} e^{\sqrt {5} t}-5 e^{\frac {1}{2} \left (1+\sqrt {5}\right ) t}-\sqrt {5}\right )-2 \sqrt {5} c_2 \left (e^{\sqrt {5} t}-1\right )+c_4 \left (\left (5+\sqrt {5}\right ) e^{\sqrt {5} t}-10 e^{\frac {1}{2} \left (1+\sqrt {5}\right ) t}+5-\sqrt {5}\right )\right ),y(t)\to \frac {1}{10} \left (\left (5+\sqrt {5}\right ) c_1-\left (5+\sqrt {5}\right ) c_2-2 \sqrt {5} c_4\right ) e^{\frac {1}{2} \left (t-\sqrt {5} t\right )}+\frac {1}{10} \left (-\left (\sqrt {5}-5\right ) c_1+\left (\sqrt {5}-5\right ) c_2+2 \sqrt {5} c_4\right ) e^{\frac {1}{2} \left (1+\sqrt {5}\right ) t}-c_1+c_2+c_3\right \}\right \}\]
✓ Maple : cpu = 0.068 (sec), leaf count = 71
\[ \left \{ \left \{ x \left ( t \right ) ={\frac {{\it \_C4}\, \left ( \sqrt {5}-1 \right ) }{2}{{\rm e}^{-{\frac { \left ( \sqrt {5}-1 \right ) t}{2}}}}}-{\frac {{\it \_C3}\, \left ( \sqrt {5}+1 \right ) }{2}{{\rm e}^{{\frac { \left ( \sqrt {5}+1 \right ) t}{2}}}}}+{\it \_C1}\,{{\rm e}^{t}},y \left ( t \right ) ={\it \_C2}+{\it \_C3}\,{{\rm e}^{{\frac { \left ( \sqrt {5}+1 \right ) t}{2}}}}+{\it \_C4}\,{{\rm e}^{-{\frac { \left ( \sqrt {5}-1 \right ) t}{2}}}} \right \} \right \} \]