\[ \left \{x''(t)+y''(t)+y'(t)=\sinh (2 t),2 x''(t)+y''(t)=2 t\right \} \] ✓ Mathematica : cpu = 0.131356 (sec), leaf count = 280
\[\left \{\left \{x(t)\to \frac {1}{4} c_4 e^{-2 t} \left (2 e^{2 t} t-e^{2 t}+1\right )+c_2 t+c_1+t \left (\frac {t^2}{2}+\frac {t}{2}-\frac {e^{4 t}}{8}+e^{2 t} \left (\frac {t}{2}-\frac {1}{4}\right )\right )+\frac {1}{48} \left (-4 \left (4 t^2-3 t+3\right ) t-12 e^{2 t} t-6 e^{-2 t}+3 e^{4 t}\right )+\frac {1}{4} e^{-2 t} \left (-2 e^{2 t} \left (\frac {t}{2}-\frac {1}{4}\right )+\frac {e^{4 t}}{4}-t\right ) \left (2 e^{2 t} t-e^{2 t}+1\right ),y(t)\to \frac {1}{2} c_4 e^{-2 t} \left (e^{2 t}-1\right )+c_3+\frac {1}{2} e^{-2 t} \left (e^{2 t}-1\right ) \left (-2 e^{2 t} \left (\frac {t}{2}-\frac {1}{4}\right )+\frac {e^{4 t}}{4}-t\right )+\frac {1}{8} e^{-2 t} \left (4 e^{4 t} t-4 e^{2 t} (t-1) t-e^{6 t}+2\right )\right \}\right \}\] ✓ Maple : cpu = 0.342 (sec), leaf count = 86
\[ \left \{ \left \{ x \left ( t \right ) ={\frac { \left ( -12\,t+12\,{\it \_C2}-15 \right ) {{\rm e}^{-2\,t}}}{48}}+{\frac {{t}^{3}}{6}}+{\frac {{t}^{2}}{4}}+{\it \_C3}\,t+{\it \_C4}-{\frac {\cosh \left ( 2\,t \right ) }{16}}-{\frac {\sinh \left ( 2\,t \right ) }{16}},y \left ( t \right ) ={\frac { \left ( 4\,t-4\,{\it \_C2}+3 \right ) {{\rm e}^{-2\,t}}}{8}}-{\frac {{t}^{2}}{2}}+{\frac {t}{2}}+{\it \_C1}+{\it \_C3}+{\frac {3\,\cosh \left ( 2\,t \right ) }{8}}-{\frac {\sinh \left ( 2\,t \right ) }{8}} \right \} \right \} \]