\[ \left \{x'(t)+y'(t)+y(t)=f(t),x''(t)+x(t)+y''(t)+y'(t)+y(t)=g(t)\right \} \] ✓ Mathematica : cpu = 0.008374 (sec), leaf count = 44
DSolve[{y[t] + Derivative[1][x][t] + Derivative[1][y][t] == f[t], x[t] + y[t] + Derivative[1][y][t] + Derivative[2][x][t] + Derivative[2][y][t] == g[t]},{x[t], y[t]},t]
\[\left \{\left \{x(t)\to -f''(t)-f'(t)-f(t)+g'(t)+g(t),y(t)\to f''(t)+f(t)-g'(t)\right \}\right \}\] ✓ Maple : cpu = 0.036 (sec), leaf count = 48
dsolve({diff(x(t),t)+diff(y(t),t)+y(t) = f(t), diff(diff(x(t),t),t)+diff(diff(y(t),t),t)+diff(y(t),t)+x(t)+y(t) = g(t)})
\[\{x \left (t \right ) = -\frac {d}{d t}f \left (t \right )+g \left (t \right )-f \left (t \right )-\frac {d^{2}}{d t^{2}}f \left (t \right )+\frac {d}{d t}g \left (t \right ), y \left (t \right ) = f \left (t \right )+\frac {d^{2}}{d t^{2}}f \left (t \right )-\frac {d}{d t}g \left (t \right )\}\]