\[ \left \{x''(t)+y''(t)+y'(t)=\sinh (2 t),2 x''(t)+y''(t)=2 t\right \} \] ✓ Mathematica : cpu = 0.109553 (sec), leaf count = 123
\[\left \{\left \{x(t)\to \frac {1}{48} e^{-2 t} \left (2 e^{2 t} \left (6 \left (4 c_2+2 c_4-1\right ) t+24 c_1-6 c_4+4 t^3+6 t^2+3\right )-6 \left (-2 c_4+2 t+1\right )-3 e^{4 t}\right ),y(t)\to \frac {1}{8} e^{-2 t} \left (e^{2 t} \left (8 c_3+4 c_4-4 t^2+4 t-2\right )-4 c_4+4 t+e^{4 t}+2\right )\right \}\right \}\]
✓ Maple : cpu = 0.169 (sec), leaf count = 86
\[ \left \{ \left \{ x \left ( t \right ) ={\frac { \left ( -12\,t+12\,{\it \_C2}-15 \right ) {{\rm e}^{-2\,t}}}{48}}+{\frac {{t}^{3}}{6}}+{\frac {{t}^{2}}{4}}+{\it \_C3}\,t+{\it \_C4}-{\frac {\cosh \left ( 2\,t \right ) }{16}}-{\frac {\sinh \left ( 2\,t \right ) }{16}},y \left ( t \right ) ={\frac { \left ( 4\,t-4\,{\it \_C2}+3 \right ) {{\rm e}^{-2\,t}}}{8}}-{\frac {{t}^{2}}{2}}+{\frac {t}{2}}+{\it \_C1}+{\it \_C3}+{\frac {3\,\cosh \left ( 2\,t \right ) }{8}}-{\frac {\sinh \left ( 2\,t \right ) }{8}} \right \} \right \} \]