\[ \left \{-t^2+x'(t)+y(t)+6 t+1=0,y'(t)-x(t)=-3 t^2+3 t+1\right \} \] ✓ Mathematica : cpu = 0.0895095 (sec), leaf count = 45
\[\left \{\left \{x(t)\to -c_2 \sin (t)+c_1 \cos (t)+3 t^2-t-13,y(t)\to c_1 \sin (t)+c_2 \cos (t)+(t-12) t\right \}\right \}\]
✓ Maple : cpu = 0.036 (sec), leaf count = 42
\[ \left \{ \left \{ x \left ( t \right ) =\sin \left ( t \right ) {\it \_C2}+\cos \left ( t \right ) {\it \_C1}+3\,{t}^{2}-t-13,y \left ( t \right ) ={t}^{2}-\cos \left ( t \right ) {\it \_C2}+\sin \left ( t \right ) {\it \_C1}-12\,t \right \} \right \} \]