\[ \left \{x'(t)-x(t)+2 y(t)=0,x''(t)-2 y'(t)=2 t-\cos (2 t)\right \} \] ✓ Mathematica : cpu = 0.40112 (sec), leaf count = 224
\[\left \{\left \{x(t)\to 7 \left (t^2-\frac {1}{2} \sin (2 t)+c_2\right )+8 \left (\frac {1}{136} e^{-t/2} \left (2 e^{t/2} \cos (2 t)-4 \left (34 e^{t/2} t^2+17 e^{t/2} (t+2)-15 e^{t/2} \sin (2 t)\right )\right )+c_1 e^{t/2}+c_2 \left (e^{t/2}-1\right )\right ),y(t)\to \frac {3}{2} \left (t^2-\frac {1}{2} \sin (2 t)+c_2\right )+2 \left (\frac {1}{136} e^{-t/2} \left (2 e^{t/2} \cos (2 t)-4 \left (34 e^{t/2} t^2+17 e^{t/2} (t+2)-15 e^{t/2} \sin (2 t)\right )\right )+c_1 e^{t/2}+c_2 \left (e^{t/2}-1\right )\right )\right \}\right \}\] ✓ Maple : cpu = 0.184 (sec), leaf count = 69
\[ \left \{ \left \{ x \left ( t \right ) =2\,{\it \_C1}\,{{\rm e}^{t/2}}-{t}^{2}+{\frac {\sin \left ( 2\,t \right ) }{34}}+{\frac {2\,\cos \left ( 2\,t \right ) }{17}}-4\,t+{\it \_C2},y \left ( t \right ) ={\frac {{\it \_C1}}{2}{{\rm e}^{{\frac {t}{2}}}}}-t+{\frac {\cos \left ( 2\,t \right ) }{34}}+{\frac {9\,\sin \left ( 2\,t \right ) }{68}}+2-{\frac {{t}^{2}}{2}}+{\frac {{\it \_C2}}{2}} \right \} \right \} \]