\[ \left \{4 x'(t)+2 x(t)+9 y'(t)+31 y(t)=e^t,3 x'(t)+x(t)+7 y'(t)+24 y(t)=3\right \} \] ✓ Mathematica : cpu = 0.305766 (sec), leaf count = 180
DSolve[{2*x[t] + 31*y[t] + 4*Derivative[1][x][t] + 9*Derivative[1][y][t] == E^t, x[t] + 24*y[t] + 3*Derivative[1][x][t] + 7*Derivative[1][y][t] == 3},{x[t], y[t]},t]
\[\left \{\left \{x(t)\to \frac {1}{442} \left (3 \left (153 e^t-754\right ) \sin (t)+31 \left (17 e^t-78\right ) \cos (t)\right ) (\cos (t)-\sin (t))+\frac {1}{221} \sin (t) \left (\left (493 e^t-2340\right ) \sin (t)+\left (34 e^t-78\right ) \cos (t)\right )-c_2 e^{-4 t} \sin (t)+c_1 e^{-4 t} (\cos (t)-\sin (t)),y(t)\to \frac {1}{221} \sin (t) \left (3 \left (153 e^t-754\right ) \sin (t)+31 \left (17 e^t-78\right ) \cos (t)\right )-\frac {1}{221} (\sin (t)+\cos (t)) \left (\left (493 e^t-2340\right ) \sin (t)+\left (34 e^t-78\right ) \cos (t)\right )+2 c_1 e^{-4 t} \sin (t)+c_2 e^{-4 t} (\sin (t)+\cos (t))\right \}\right \}\] ✓ Maple : cpu = 0.098 (sec), leaf count = 62
dsolve({3*diff(x(t),t)+7*diff(y(t),t)+x(t)+24*y(t) = 3, 4*diff(x(t),t)+9*diff(y(t),t)+2*x(t)+31*y(t) = exp(t)})
\[\left \{x \left (t \right ) = {\mathrm e}^{-4 t} \sin \left (t \right ) c_{2}+{\mathrm e}^{-4 t} \cos \left (t \right ) c_{1}-\frac {93}{17}+\frac {31 \,{\mathrm e}^{t}}{26}, y \left (t \right ) = \frac {\left (\left (-221 c_{1}-221 c_{2}\right ) \cos \left (t \right )+221 \sin \left (t \right ) \left (c_{1}-c_{2}\right )\right ) {\mathrm e}^{-4 t}}{221}-\frac {2 \,{\mathrm e}^{t}}{13}+\frac {6}{17}\right \}\]