\[ \left \{4 x'(t)+11 x(t)+9 y'(t)+31 y(t)=e^t,3 x'(t)+8 x(t)+7 y'(t)+24 y(t)=e^{2 t}\right \} \] ✓ Mathematica : cpu = 0.109811 (sec), leaf count = 162
DSolve[{11*x[t] + 31*y[t] + 4*Derivative[1][x][t] + 9*Derivative[1][y][t] == E^t, 8*x[t] + 24*y[t] + 3*Derivative[1][x][t] + 7*Derivative[1][y][t] == E^(2*t)},{x[t], y[t]},t]
\[\left \{\left \{x(t)\to -e^t t \left (-\frac {4 t}{5}+\frac {1}{36} e^t (30 t+19)-\frac {11}{25}\right )-e^t (t-1) \left (\frac {4 t}{5}-\frac {1}{36} e^t (30 t+49)+\frac {31}{25}\right )-c_1 e^{-4 t} (t-1)-c_2 e^{-4 t} t,y(t)\to e^t (t+1) \left (-\frac {4 t}{5}+\frac {1}{36} e^t (30 t+19)-\frac {11}{25}\right )+e^t t \left (\frac {4 t}{5}-\frac {1}{36} e^t (30 t+49)+\frac {31}{25}\right )+c_1 e^{-4 t} t+c_2 e^{-4 t} (t+1)\right \}\right \}\] ✓ Maple : cpu = 0.078 (sec), leaf count = 65
dsolve({3*diff(x(t),t)+7*diff(y(t),t)+8*x(t)+24*y(t) = exp(2*t), 4*diff(x(t),t)+9*diff(y(t),t)+11*x(t)+31*y(t) = exp(t)})
\[\left \{x \left (t \right ) = {\mathrm e}^{-4 t} c_{2}+{\mathrm e}^{-4 t} t c_{1}+\frac {31 \,{\mathrm e}^{t}}{25}-\frac {49 \,{\mathrm e}^{2 t}}{36}, y \left (t \right ) = \frac {19 \,{\mathrm e}^{2 t}}{36}-{\mathrm e}^{-4 t} c_{2}-{\mathrm e}^{-4 t} t c_{1}-{\mathrm e}^{-4 t} c_{1}-\frac {11 \,{\mathrm e}^{t}}{25}\right \}\]