\[ \left \{x'(t)-x(t)+2 y(t)=0,x''(t)-2 y'(t)=2 t-\cos (2 t)\right \} \] ✓ Mathematica : cpu = 0.404414 (sec), leaf count = 224
DSolve[{-x[t] + 2*y[t] + Derivative[1][x][t] == 0, -2*Derivative[1][y][t] + Derivative[2][x][t] == 2*t - Cos[2*t]},{x[t], y[t]},t]
\[\left \{\left \{x(t)\to 7 \left (t^2-\frac {1}{2} \sin (2 t)+c_2\right )+8 \left (\frac {1}{136} e^{-t/2} \left (2 e^{t/2} \cos (2 t)-4 \left (34 e^{t/2} t^2+17 e^{t/2} (t+2)-15 e^{t/2} \sin (2 t)\right )\right )+c_1 e^{t/2}+c_2 \left (e^{t/2}-1\right )\right ),y(t)\to \frac {3}{2} \left (t^2-\frac {1}{2} \sin (2 t)+c_2\right )+2 \left (\frac {1}{136} e^{-t/2} \left (2 e^{t/2} \cos (2 t)-4 \left (34 e^{t/2} t^2+17 e^{t/2} (t+2)-15 e^{t/2} \sin (2 t)\right )\right )+c_1 e^{t/2}+c_2 \left (e^{t/2}-1\right )\right )\right \}\right \}\] ✓ Maple : cpu = 0.134 (sec), leaf count = 69
dsolve({diff(diff(x(t),t),t)-2*diff(y(t),t) = 2*t-cos(2*t), diff(x(t),t)-x(t)+2*y(t) = 0})
\[\left \{x \left (t \right ) = 2 c_{1} {\mathrm e}^{\frac {t}{2}}-t^{2}+\frac {\sin \left (2 t \right )}{34}+\frac {2 \cos \left (2 t \right )}{17}-4 t +c_{2}, y \left (t \right ) = \frac {c_{1} {\mathrm e}^{\frac {t}{2}}}{2}-t +\frac {\cos \left (2 t \right )}{34}+\frac {9 \sin \left (2 t \right )}{68}+2-\frac {t^{2}}{2}+\frac {c_{2}}{2}\right \}\]