\[ \left \{x'(t)+3 x(t)-y(t)=e^{2 t},x(t)+y'(t)+5 y(t)=e^t\right \} \] ✓ Mathematica : cpu = 0.0779975 (sec), leaf count = 162
DSolve[{3*x[t] - y[t] + Derivative[1][x][t] == E^(2*t), x[t] + 5*y[t] + Derivative[1][y][t] == E^t},{x[t], y[t]},t]
\[\left \{\left \{x(t)\to -e^t (t+1) \left (\frac {t}{5}+\frac {1}{36} e^t (6 t-7)-\frac {1}{25}\right )+e^t t \left (\frac {t}{5}+\frac {1}{36} e^t (6 t-1)+\frac {4}{25}\right )+c_1 e^{-4 t} (t+1)+c_2 e^{-4 t} t,y(t)\to e^t t \left (\frac {t}{5}+\frac {1}{36} e^t (6 t-7)-\frac {1}{25}\right )-e^t (t-1) \left (\frac {t}{5}+\frac {1}{36} e^t (6 t-1)+\frac {4}{25}\right )-c_1 e^{-4 t} t-c_2 e^{-4 t} (t-1)\right \}\right \}\] ✓ Maple : cpu = 0.083 (sec), leaf count = 64
dsolve({diff(x(t),t)+3*x(t)-y(t) = exp(2*t), diff(y(t),t)+x(t)+5*y(t) = exp(t)})
\[\left \{x \left (t \right ) = {\mathrm e}^{-4 t} c_{2}+{\mathrm e}^{-4 t} t c_{1}+\frac {{\mathrm e}^{t}}{25}+\frac {7 \,{\mathrm e}^{2 t}}{36}, y \left (t \right ) = -\frac {{\mathrm e}^{2 t}}{36}-{\mathrm e}^{-4 t} c_{2}-{\mathrm e}^{-4 t} t c_{1}+{\mathrm e}^{-4 t} c_{1}+\frac {4 \,{\mathrm e}^{t}}{25}\right \}\]