\[ \left \{4 x'(t)+44 x(t)+9 y'(t)+49 y(t)=t,3 x'(t)+34 x(t)+7 y'(t)+38 y(t)=e^t\right \} \] ✓ Mathematica : cpu = 0.087659 (sec), leaf count = 322
DSolve[{44*x[t] + 49*y[t] + 4*Derivative[1][x][t] + 9*Derivative[1][y][t] == t, 34*x[t] + 38*y[t] + 3*Derivative[1][x][t] + 7*Derivative[1][y][t] == E^t},{x[t], y[t]},t]
\[\left \{\left \{x(t)\to -\frac {1}{5} e^{-6 t} \left (e^{5 t}-1\right ) \left (\frac {16}{5} e^{6 t} \left (\frac {t}{6}-\frac {1}{36}\right )+4 e^{2 t}-\frac {4 e^{7 t}}{7}-\frac {31}{5} e^t (t-1)\right )+\frac {1}{25} e^{-6 t} \left (4 e^{5 t}+1\right ) \left (e^{6 t} \left (\frac {2 t}{3}-\frac {1}{9}\right )-20 e^{2 t}-\frac {5 e^{7 t}}{7}+e^t (31 t-31)\right )+\frac {1}{5} c_1 e^{-6 t} \left (4 e^{5 t}+1\right )-\frac {1}{5} c_2 e^{-6 t} \left (e^{5 t}-1\right ),y(t)\to \frac {1}{5} e^{-6 t} \left (e^{5 t}+4\right ) \left (\frac {16}{5} e^{6 t} \left (\frac {t}{6}-\frac {1}{36}\right )+4 e^{2 t}-\frac {4 e^{7 t}}{7}-\frac {31}{5} e^t (t-1)\right )-\frac {4}{25} e^{-6 t} \left (e^{5 t}-1\right ) \left (e^{6 t} \left (\frac {2 t}{3}-\frac {1}{9}\right )-20 e^{2 t}-\frac {5 e^{7 t}}{7}+e^t (31 t-31)\right )-\frac {4}{5} c_1 e^{-6 t} \left (e^{5 t}-1\right )+\frac {1}{5} c_2 e^{-6 t} \left (e^{5 t}+4\right )\right \}\right \}\] ✓ Maple : cpu = 0.074 (sec), leaf count = 52
dsolve({3*diff(x(t),t)+7*diff(y(t),t)+34*x(t)+38*y(t) = exp(t), 4*diff(x(t),t)+9*diff(y(t),t)+44*x(t)+49*y(t) = t})
\[\left \{x \left (t \right ) = {\mathrm e}^{-t} c_{2}+{\mathrm e}^{-6 t} c_{1}-\frac {29 \,{\mathrm e}^{t}}{7}+\frac {19 t}{3}-\frac {56}{9}, y \left (t \right ) = -{\mathrm e}^{-t} c_{2}+4 \,{\mathrm e}^{-6 t} c_{1}+\frac {24 \,{\mathrm e}^{t}}{7}+\frac {55}{9}-\frac {17 t}{3}\right \}\]