\[ \left \{2 x'(t)-3 x(t)+y'(t)=0,x''(t)+y'(t)-2 y(t)=e^{2 t}\right \} \] ✓ Mathematica : cpu = 0.594345 (sec), leaf count = 199
\[\left \{\left \{x(t)\to \frac {1}{276} e^{t/2} \left (23 e^{t/2} \left (6 c_1+2 c_2+4 c_3+3 e^t\right )-2 \sqrt {23} \left (9 c_1-11 c_2+2 c_3\right ) \sin \left (\frac {\sqrt {23} t}{2}\right )+46 \left (3 c_1-c_2-2 c_3\right ) \cos \left (\frac {\sqrt {23} t}{2}\right )\right ),y(t)\to -\frac {1}{552} e^{t/2} \left (23 e^{t/2} \left (3 e^t-4 \left (3 c_1+c_2+2 c_3\right )\right )-4 \sqrt {23} \left (33 c_1-25 c_2-8 c_3\right ) \sin \left (\frac {\sqrt {23} t}{2}\right )+92 \left (3 c_1+c_2-4 c_3\right ) \cos \left (\frac {\sqrt {23} t}{2}\right )\right )\right \}\right \}\]
✓ Maple : cpu = 0.169 (sec), leaf count = 99
\[ \left \{ \left \{ x \left ( t \right ) ={\frac {{{\rm e}^{2\,t}}}{4}}+{\it \_C1}\,{{\rm e}^{t}}+{\it \_C2}\,{{\rm e}^{{\frac {t}{2}}}}\cos \left ( {\frac {\sqrt {23}t}{2}} \right ) +{\it \_C3}\,{{\rm e}^{{\frac {t}{2}}}}\sin \left ( {\frac {\sqrt {23}t}{2}} \right ) ,y \left ( t \right ) =-{\frac {7}{4} \left ( {\frac {{\it \_C3}\,\sqrt {23}}{7}}+{\it \_C2} \right ) {{\rm e}^{{\frac {t}{2}}}}\cos \left ( {\frac {\sqrt {23}t}{2}} \right ) }+{\frac {{\it \_C2}\,\sqrt {23}-7\,{\it \_C3}}{4}{{\rm e}^{{\frac {t}{2}}}}\sin \left ( {\frac {\sqrt {23}t}{2}} \right ) }+{\it \_C1}\,{{\rm e}^{t}}-{\frac {{{\rm e}^{2\,t}}}{8}} \right \} \right \} \]