10.36   ODE No. 1891

$$\boxed{{\displaystyle \{\frac{{\mathrm{d}}^2}{\mathrm{d}{t}^2}x\left(t\right)+6x\left(t\right)+7y\left(t\right)=0,\frac{{\mathrm{d}}^2}{\mathrm{d}{t}^2}y\left(t\right)+3x\left(t\right)+2y\left(t\right)=2t\}}}$$

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

Mathematica: cpu = 0.445557 (sec), leaf count = 766 $$\left\{\{x(t)\to -\frac{7}{60}{c}_4{e}^{-t}(3e^{2t}-2e^t\sin (3t)-3)+\frac{1}{60}{c}_2{e}^{-t}(9e^{2t}+14e^t\sin (3t)-9)-\frac{7}{20}{c}_3{e}^{-t}(e^{2t}-2e^t\cos (3t)+1)+\frac{1}{20}{c}_1{e}^{-t}(3e^{2t}+14e^t\cos (3t)+3)-\frac{7}{200}{e}^{-t}(e^{2t}-2e^t\cos (3t)+1)(-\frac{7}{3}{e}^t(3e^{-2t}t+3t+3e^{-2t}-3)-\frac{2}{9}\sin (3t)+\frac{2}{3}t\cos (3t))+\frac{7}{600}{e}^{-t}(3e^{2t}+14e^t\cos (3t)+3)(3e^{-t}(e^{2t}(t-1)+t+1)-\frac{2}{9}\sin (3t)+\frac{2}{3}t\cos (3t))-\frac{7}{600}{e}^{-t}(9e^{2t}+14e^t\sin (3t)-9)(e^{-t}(e^{2t}(t-1)-t-1)-\frac{2}{3}t\sin (3t)-\frac{2}{9}\cos (3t))-\frac{7}{600}{e}^{-t}(3e^{2t}-2e^t\sin (3t)-3)(e^{-t}(7e^{2t}(t-1)-7(t+1))+2t\sin (3t)+\frac{2}{3}\cos (3t)),y(t)\to -\frac{1}{20}{c}_2{e}^{-t}(3e^{2t}-2e^t\sin (3t)-3)+\frac{1}{20}{c}_4{e}^{-t}(7e^{2t}+2e^t\sin (3t)-7)-\frac{3}{20}{c}_1{e}^{-t}(e^{2t}-2e^t\cos (3t)+1)+\frac{1}{20}{c}_3{e}^{-t}(7e^{2t}+6e^t\cos (3t)+7)-\frac{7}{200}{e}^{-t}(e^{2t}-2e^t\cos (3t)+1)(3e^{-t}(e^{2t}(t-1)+t+1)-\frac{2}{9}\sin (3t)+\frac{2}{3}t\cos (3t))+\frac{1}{200}{e}^{-t}(7e^{2t}+6e^t\cos (3t)+7)(-\frac{7}{3}{e}^t(3e^{-2t}t+3t+3e^{-2t}-3)-\frac{2}{9}\sin (3t)+\frac{2}{3}t\cos (3t))+\frac{7}{200}{e}^{-t}(3e^{2t}-2e^t\sin (3t)-3)(e^{-t}(e^{2t}(t-1)-t-1)-\frac{2}{3}t\sin (3t)-\frac{2}{9}\cos (3t))+\frac{1}{200}{e}^{-t}(7e^{2t}+2e^t\sin (3t)-7)(e^{-t}(7e^{2t}(t-1)-7(t+1))+2t\sin (3t)+\frac{2}{3}\cos (3t))\}\right\}$$

Maple: cpu = 0.047 (sec), leaf count = 64 $$\left\{\{x\left(t\right)=\frac{14t}{9}+\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^t+\mathit{\_}\mathit{C}\mathit{2}\cos \left(3t\right)+\mathit{\_}\mathit{C}\mathit{3}{\mathrm{e}}^{-t}+\mathit{\_}\mathit{C}\mathit{4}\sin \left(3t\right),y\left(t\right)=-\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^t+\frac{3\mathit{\_}\mathit{C}\mathit{2}\cos \left(3t\right)}{7}-\mathit{\_}\mathit{C}\mathit{3}{\mathrm{e}}^{-t}+\frac{3\mathit{\_}\mathit{C}\mathit{4}\sin \left(3t\right)}{7}-\frac{4t}{3}\}\right\}$$