\[ \left \{2 x'(t)-3 x(t)+y'(t)=0,x''(t)+y'(t)-2 y(t)=e^{2 t}\right \} \] ✓ Mathematica : cpu = 1.53659 (sec), leaf count = 928
\[\left \{\left \{x(t)\to \frac {1}{46} e^{t/2} c_1 \left (23 \cos \left (\frac {\sqrt {23} t}{2}\right )+23 e^{t/2}-3 \sqrt {23} \sin \left (\frac {\sqrt {23} t}{2}\right )\right )+\frac {e^{3 t/2} \left (23 e^{t/2} \cos \left (\frac {\sqrt {23} t}{2}\right )-7 \sqrt {23} e^{t/2} \sin \left (\frac {\sqrt {23} t}{2}\right )+46\right ) \left (23 \cos \left (\frac {\sqrt {23} t}{2}\right )+23 e^{t/2}-3 \sqrt {23} \sin \left (\frac {\sqrt {23} t}{2}\right )\right )}{12696}+\frac {1}{69} e^{t/2} c_3 \left (-23 \cos \left (\frac {\sqrt {23} t}{2}\right )+23 e^{t/2}-\sqrt {23} \sin \left (\frac {\sqrt {23} t}{2}\right )\right )+\frac {1}{138} e^{t/2} c_2 \left (-23 \cos \left (\frac {\sqrt {23} t}{2}\right )+23 e^{t/2}+11 \sqrt {23} \sin \left (\frac {\sqrt {23} t}{2}\right )\right )+\frac {e^{3 t/2} \left (-23 \cos \left (\frac {\sqrt {23} t}{2}\right )+23 e^{t/2}+11 \sqrt {23} \sin \left (\frac {\sqrt {23} t}{2}\right )\right ) \left (46 e^{t/2} \cos \left (\frac {\sqrt {23} t}{2}\right )+4 \sqrt {23} e^{t/2} \sin \left (\frac {\sqrt {23} t}{2}\right )+23\right )}{19044}+\frac {e^{3 t/2} \left (-23 \cos \left (\frac {\sqrt {23} t}{2}\right )+23 e^{t/2}-\sqrt {23} \sin \left (\frac {\sqrt {23} t}{2}\right )\right ) \left (-161 e^{t/2} \cos \left (\frac {\sqrt {23} t}{2}\right )+13 \sqrt {23} e^{t/2} \sin \left (\frac {\sqrt {23} t}{2}\right )+92\right )}{38088},y(t)\to \frac {1}{138} e^{t/2} c_2 \left (-23 \cos \left (\frac {\sqrt {23} t}{2}\right )+23 e^{t/2}-25 \sqrt {23} \sin \left (\frac {\sqrt {23} t}{2}\right )\right )+\frac {e^{3 t/2} \left (46 e^{t/2} \cos \left (\frac {\sqrt {23} t}{2}\right )+4 \sqrt {23} e^{t/2} \sin \left (\frac {\sqrt {23} t}{2}\right )+23\right ) \left (-23 \cos \left (\frac {\sqrt {23} t}{2}\right )+23 e^{t/2}-25 \sqrt {23} \sin \left (\frac {\sqrt {23} t}{2}\right )\right )}{19044}+\frac {1}{69} e^{t/2} c_3 \left (46 \cos \left (\frac {\sqrt {23} t}{2}\right )+23 e^{t/2}-4 \sqrt {23} \sin \left (\frac {\sqrt {23} t}{2}\right )\right )+\frac {1}{46} e^{t/2} c_1 \left (-23 \cos \left (\frac {\sqrt {23} t}{2}\right )+23 e^{t/2}+11 \sqrt {23} \sin \left (\frac {\sqrt {23} t}{2}\right )\right )+\frac {e^{3 t/2} \left (-23 \cos \left (\frac {\sqrt {23} t}{2}\right )+23 e^{t/2}+11 \sqrt {23} \sin \left (\frac {\sqrt {23} t}{2}\right )\right ) \left (23 e^{t/2} \cos \left (\frac {\sqrt {23} t}{2}\right )-7 \sqrt {23} e^{t/2} \sin \left (\frac {\sqrt {23} t}{2}\right )+46\right )}{12696}+\frac {e^{3 t/2} \left (46 \cos \left (\frac {\sqrt {23} t}{2}\right )+23 e^{t/2}-4 \sqrt {23} \sin \left (\frac {\sqrt {23} t}{2}\right )\right ) \left (-161 e^{t/2} \cos \left (\frac {\sqrt {23} t}{2}\right )+13 \sqrt {23} e^{t/2} \sin \left (\frac {\sqrt {23} t}{2}\right )+92\right )}{38088}\right \}\right \}\] ✓ Maple : cpu = 0.07 (sec), leaf count = 99
\[ \left \{ \left \{ x \left ( t \right ) ={\frac {{{\rm e}^{2\,t}}}{4}}+{\it \_C1}\,{{\rm e}^{t}}+{\it \_C2}\,{{\rm e}^{{\frac {t}{2}}}}\cos \left ( {\frac {\sqrt {23}t}{2}} \right ) +{\it \_C3}\,{{\rm e}^{{\frac {t}{2}}}}\sin \left ( {\frac {\sqrt {23}t}{2}} \right ) ,y \left ( t \right ) =-{\frac {7}{4} \left ( {\frac {{\it \_C3}\,\sqrt {23}}{7}}+{\it \_C2} \right ) {{\rm e}^{{\frac {t}{2}}}}\cos \left ( {\frac {\sqrt {23}t}{2}} \right ) }+{\frac {{\it \_C2}\,\sqrt {23}-7\,{\it \_C3}}{4}{{\rm e}^{{\frac {t}{2}}}}\sin \left ( {\frac {\sqrt {23}t}{2}} \right ) }+{\it \_C1}\,{{\rm e}^{t}}-{\frac {{{\rm e}^{2\,t}}}{8}} \right \} \right \} \]