10.42   ODE No. 1897

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

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

Mathematica: cpu = 0.114015 (sec), leaf count = 284 $$\left\{\{x(t)\to \frac{1}{4}{c}_4{e}^{-2t}(2e^{2t}t-e^{2t}+1)+c_{2}t+c_1+t(\frac{t^2}{2}+\frac{t}{2}-\frac{e^{4t}}{8}+e^{2t}(\frac{t}{2}-\frac{1}{4}))+\frac{1}{48}{e}^{-2t}(-4e^{2t}(4t^2-3t+3)t-12e^{4t}t+3e^{6t}-6)+\frac{1}{4}{e}^{-2t}(-2e^{2t}(\frac{t}{2}-\frac{1}{4})+\frac{e^{4t}}{4}-t)(2e^{2t}t-e^{2t}+1),y(t)\to \frac{1}{2}{c}_4{e}^{-2t}(e^{2t}-1)+c_3+\frac{1}{2}{e}^{-2t}(e^{2t}-1)(-2e^{2t}(\frac{t}{2}-\frac{1}{4})+\frac{e^{4t}}{4}-t)+\frac{1}{8}{e}^{-2t}(4e^{4t}t-4e^{2t}(t-1)t-e^{6t}+2)\}\right\}$$

Maple: cpu = 0.110 (sec), leaf count = 98 $$\left\{\{x\left(t\right)=-\frac{\sinh \left(2t\right)}{16}-\frac{\cosh \left(2t\right)}{16}-\frac{5{\mathrm{e}}^{-2t}}{16}-\frac{{\mathrm{e}}^{-2t}t}{4}+\frac{t^3}{6}+\frac{{\mathrm{e}}^{-2t}\mathit{\_}\mathit{C}\mathit{2}}{4}+\frac{t^2}{4}+\mathit{\_}\mathit{C}\mathit{3}t+\mathit{\_}\mathit{C}\mathit{4},y\left(t\right)=\frac{3\cosh \left(2t\right)}{8}-\frac{\sinh \left(2t\right)}{8}+\frac{3{\mathrm{e}}^{-2t}}{8}+\frac{{\mathrm{e}}^{-2t}t}{2}-\frac{t^2}{2}-\frac{{\mathrm{e}}^{-2t}\mathit{\_}\mathit{C}\mathit{2}}{2}+\frac{t}{2}+\mathit{\_}\mathit{C}\mathit{3}+\mathit{\_}\mathit{C}\mathit{1}\}\right\}$$