\[ \left \{-t^2+x'(t)+y(t)+6 t+1=0,y'(t)-x(t)=-3 t^2+3 t+1\right \} \] ✓ Mathematica : cpu = 0.0878752 (sec), leaf count = 124
\[\left \{\left \{x(t)\to -c_2 \sin (t)+c_1 \cos (t)+\cos (t) \left (\left (3 t^2-t-13\right ) \cos (t)+(t-12) t \sin (t)\right )-\sin (t) \left (\left (-3 t^2+t+13\right ) \sin (t)+(t-12) t \cos (t)\right ),y(t)\to c_1 \sin (t)+c_2 \cos (t)+\cos (t) \left (\left (-3 t^2+t+13\right ) \sin (t)+(t-12) t \cos (t)\right )+\sin (t) \left (\left (3 t^2-t-13\right ) \cos (t)+(t-12) t \sin (t)\right )\right \}\right \}\] ✓ Maple : cpu = 0.026 (sec), leaf count = 42
\[ \left \{ \left \{ x \left ( t \right ) =\sin \left ( t \right ) {\it \_C2}+\cos \left ( t \right ) {\it \_C1}+3\,{t}^{2}-t-13,y \left ( t \right ) ={t}^{2}-\cos \left ( t \right ) {\it \_C2}+\sin \left ( t \right ) {\it \_C1}-12\,t \right \} \right \} \]