\[ \left \{x'(t)+x(t)-y'(t)=2 t,x''(t)-9 x(t)+y'(t)+3 y(t)=\sin (2 t)\right \} \] ✓ Mathematica : cpu = 0.878258 (sec), leaf count = 602
\[\left \{\left \{x(t)\to \frac {e^{-4 t} \left (20 e^{4 t} t+7 e^{4 t}+9\right ) \left (10400 \left (t^2+2 t+2\right )+\left (260 t-225 e^{4 t}-351\right ) \sin (2 t)+2 \left (260 t+75 e^{4 t}-91\right ) \cos (2 t)\right )}{83200}-\frac {3 e^{-4 t} \left (4 e^{4 t} t-e^{4 t}+1\right ) \left (5200 \left (2 t^2+5 t+5\right )+\left (260 t-75 e^{4 t}-221\right ) \sin (2 t)+\left (520 t+50 e^{4 t}+78\right ) \cos (2 t)\right )}{41600}+\frac {e^{-4 t} \left (4 e^{4 t} t+3 e^{4 t}-3\right ) \left (10400 \left (t^2+t+1\right )+\left (260 t+675 e^{4 t}-611\right ) \sin (2 t)+\left (520 t-450 e^{4 t}-702\right ) \cos (2 t)\right )}{83200}+\frac {1}{16} c_1 e^{-3 t} \left (20 e^{4 t} t+7 e^{4 t}+9\right )+\frac {1}{16} c_2 e^{-3 t} \left (4 e^{4 t} t+3 e^{4 t}-3\right )-\frac {3}{16} c_3 e^{-3 t} \left (4 e^{4 t} t-e^{4 t}+1\right ),y(t)\to \frac {e^{-4 t} \left (20 e^{4 t} t-3 e^{4 t}+3\right ) \left (10400 \left (t^2+2 t+2\right )+\left (260 t-225 e^{4 t}-351\right ) \sin (2 t)+2 \left (260 t+75 e^{4 t}-91\right ) \cos (2 t)\right )}{41600}-\frac {e^{-4 t} \left (12 e^{4 t} t-9 e^{4 t}+1\right ) \left (5200 \left (2 t^2+5 t+5\right )+\left (260 t-75 e^{4 t}-221\right ) \sin (2 t)+\left (520 t+50 e^{4 t}+78\right ) \cos (2 t)\right )}{20800}+\frac {e^{-4 t} \left (4 e^{4 t} t+e^{4 t}-1\right ) \left (10400 \left (t^2+t+1\right )+\left (260 t+675 e^{4 t}-611\right ) \sin (2 t)+\left (520 t-450 e^{4 t}-702\right ) \cos (2 t)\right )}{41600}+\frac {1}{8} c_1 e^{-3 t} \left (20 e^{4 t} t-3 e^{4 t}+3\right )+\frac {1}{8} c_2 e^{-3 t} \left (4 e^{4 t} t+e^{4 t}-1\right )-\frac {1}{8} c_3 e^{-3 t} \left (12 e^{4 t} t-9 e^{4 t}+1\right )\right \}\right \}\] ✓ Maple : cpu = 0.121 (sec), leaf count = 80
\[\left \{x \relax (t ) = 4+2 t -\frac {36 \sin \left (2 t \right )}{325}-\frac {2 \cos \left (2 t \right )}{325}+c_{1} {\mathrm e}^{t}+c_{2} {\mathrm e}^{-3 t}+c_{3} {\mathrm e}^{t} t, y \relax (t ) = -\frac {37 \sin \left (2 t \right )}{325}+\frac {16 \cos \left (2 t \right )}{325}+2 c_{1} {\mathrm e}^{t}+\frac {2 c_{2} {\mathrm e}^{-3 t}}{3}+2 c_{3} {\mathrm e}^{t} t -c_{3} {\mathrm e}^{t}+10+6 t\right \}\]