10.12   ODE No. 1867

$$\boxed{{\displaystyle \{\frac{\mathrm{d}}{\mathrm{d}t}y\left(t\right)-x\left(t\right)=-3t^2+3t+1,\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)+y\left(t\right)-t^2+6t+1=0\}}}$$

1. Problem in Latex
2. Mathematica input
3. Maple input

Mathematica: cpu = 0.075510 (sec), leaf count = 124 $$\left\{\{x(t)\to -c_2\sin (t)+c_1\cos (t)+\cos (t)((3t^2-t-13)\cos (t)+(t-12)t\sin (t))-\sin (t)((-3t^2+t+13)\sin (t)+(t-12)t\cos (t)),y(t)\to c_1\sin (t)+c_2\cos (t)+\cos (t)((-3t^2+t+13)\sin (t)+(t-12)t\cos (t))+\sin (t)((3t^2-t-13)\cos (t)+(t-12)t\sin (t))\}\right\}$$

Maple: cpu = 0.031 (sec), leaf count = 42 $$\left\{\{x\left(t\right)=\sin \left(t\right)\mathit{\_}\mathit{C}\mathit{2}+\cos \left(t\right)\mathit{\_}\mathit{C}\mathit{1}+3t^2-t-13,y\left(t\right)=t^2-\cos \left(t\right)\mathit{\_}\mathit{C}\mathit{2}+\sin \left(t\right)\mathit{\_}\mathit{C}\mathit{1}-12t\}\right\}$$