\[ \left \{x''(t)+y''(t)+y'(t)=\sinh (2 t),2 x''(t)+y''(t)=2 t\right \} \] ✓ Mathematica : cpu = 0.210661 (sec), leaf count = 280
DSolve[{Derivative[1][y][t] + Derivative[2][x][t] + Derivative[2][y][t] == Sinh[2*t], 2*Derivative[2][x][t] + Derivative[2][y][t] == 2*t},{x[t], y[t]},t]
\[\left \{\left \{x(t)\to t \left (\frac {t^2}{2}+\frac {t}{2}-\frac {e^{4 t}}{8}+e^{2 t} \left (\frac {t}{2}-\frac {1}{4}\right )\right )+\frac {1}{48} \left (-4 \left (4 t^2-3 t+3\right ) t-12 e^{2 t} t-6 e^{-2 t}+3 e^{4 t}\right )+\frac {1}{4} e^{-2 t} \left (-2 e^{2 t} \left (\frac {t}{2}-\frac {1}{4}\right )+\frac {e^{4 t}}{4}-t\right ) \left (2 e^{2 t} t-e^{2 t}+1\right )+\frac {1}{4} c_4 e^{-2 t} \left (2 e^{2 t} t-e^{2 t}+1\right )+c_2 t+c_1,y(t)\to \frac {1}{2} e^{-2 t} \left (e^{2 t}-1\right ) \left (-2 e^{2 t} \left (\frac {t}{2}-\frac {1}{4}\right )+\frac {e^{4 t}}{4}-t\right )+\frac {1}{8} e^{-2 t} \left (4 e^{4 t} t-4 e^{2 t} (t-1) t-e^{6 t}+2\right )+\frac {1}{2} c_4 e^{-2 t} \left (e^{2 t}-1\right )+c_3\right \}\right \}\] ✓ Maple : cpu = 0.28 (sec), leaf count = 90
dsolve({2*diff(diff(x(t),t),t)+diff(diff(y(t),t),t) = 2*t, diff(diff(x(t),t),t)+diff(diff(y(t),t),t)+diff(y(t),t) = sinh(2*t)})
\[\left \{x \left (t \right ) = \frac {\left (6 c_{2}-6 t -9\right ) \cosh \left (2 t \right )}{24}+\frac {\left (-6 c_{2}+6 t +6\right ) \sinh \left (2 t \right )}{24}+\frac {t^{3}}{6}+\frac {t^{2}}{4}+t c_{3}+c_{4}, y \left (t \right ) = \frac {\left (-2 c_{2}+2 t +3\right ) \cosh \left (2 t \right )}{4}+\frac {\left (2 c_{2}-2 t -2\right ) \sinh \left (2 t \right )}{4}-\frac {t^{2}}{2}+\frac {t}{2}+c_{1}+c_{3}\right \}\]