10.14   ODE No. 1869

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

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

Mathematica: cpu = 0.087511 (sec), leaf count = 118 $$\left\{\{x(t)\to \frac{5}{72}(c_1{e}^{-7t/5}+\frac{12(5712t+833e^t+2352e^{2t}-5508)}{20825})+\frac{1}{5}(t-e^t+e^{2t}+1),y(t)\to \frac{5}{48}(c_1{e}^{-7t/5}+\frac{12(5712t+833e^t+2352e^{2t}-5508)}{20825})+\frac{1}{5}(-t+e^t-e^{2t}-1)\}\right\}$$

Maple: cpu = 0.031 (sec), leaf count = 51 $$\left\{\{x\left(t\right)=\frac{5{\mathrm{e}}^{2t}}{17}-\frac{{\mathrm{e}}^t}{6}+\frac{3t}{7}-\frac{1}{49}+{\mathrm{e}}^{-\frac{7t}{5}}\mathit{\_}\mathit{C}\mathit{1},y\left(t\right)=-\frac{{\mathrm{e}}^{2t}}{17}+\frac{{\mathrm{e}}^t}{4}+\frac{t}{7}-\frac{26}{49}+\frac{3\mathit{\_}\mathit{C}\mathit{1}}{2}{\mathrm{e}}^{-\frac{7t}{5}}\}\right\}$$