\[ \left \{2 x'(t)-3 x(t)+y'(t)=0,x''(t)+y'(t)-2 y(t)=e^{2 t}\right \} \] ✓ Mathematica : cpu = 1.73687 (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 = 0.235 (sec), leaf count = 99
\[\left \{\left \{x \left (t \right ) = c_{2} \cos \left (\frac {\sqrt {23}\, t}{2}\right ) {\mathrm e}^{\frac {t}{2}}+c_{3} {\mathrm e}^{\frac {t}{2}} \sin \left (\frac {\sqrt {23}\, t}{2}\right )+c_{1} {\mathrm e}^{t}+\frac {{\mathrm e}^{2 t}}{4}, y \left (t \right ) = c_{1} {\mathrm e}^{t}-\frac {7 \left (c_{2}+\frac {c_{3} \sqrt {23}}{7}\right ) \cos \left (\frac {\sqrt {23}\, t}{2}\right ) {\mathrm e}^{\frac {t}{2}}}{4}+\frac {\left (c_{2} \sqrt {23}-7 c_{3}\right ) {\mathrm e}^{\frac {t}{2}} \sin \left (\frac {\sqrt {23}\, t}{2}\right )}{4}-\frac {{\mathrm e}^{2 t}}{8}\right \}\right \}\]