10.17   ODE No. 1872

$$\boxed{{\displaystyle \{3\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)+7\frac{\mathrm{d}}{\mathrm{d}t}y\left(t\right)+8x\left(t\right)+24y\left(t\right)={\mathrm{e}}^{2t},4\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)+9\frac{\mathrm{d}}{\mathrm{d}t}y\left(t\right)+11x\left(t\right)+31y\left(t\right)={\mathrm{e}}^t\}}}$$

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

Mathematica: cpu = 0.059508 (sec), leaf count = 162 $$\left\{\{x(t)\to -c_1{e}^{-4t}(t-1)-c_2{e}^{-4t}t-e^{t}t(-\frac{4t}{5}+\frac{1}{36}{e}^t(30t+19)-\frac{11}{25})-e^t(t-1)(\frac{4t}{5}-\frac{1}{36}{e}^t(30t+49)+\frac{31}{25}),y(t)\to c_1{e}^{-4t}t+c_2{e}^{-4t}(t+1)+e^t(t+1)(-\frac{4t}{5}+\frac{1}{36}{e}^t(30t+19)-\frac{11}{25})+e^{t}t(\frac{4t}{5}-\frac{1}{36}{e}^t(30t+49)+\frac{31}{25})\}\right\}$$

Maple: cpu = 0.047 (sec), leaf count = 65 $$\left\{\{x\left(t\right)={\mathrm{e}}^{-4t}\mathit{\_}\mathit{C}\mathit{2}+{\mathrm{e}}^{-4t}t\mathit{\_}\mathit{C}\mathit{1}-\frac{49{\mathrm{e}}^{2t}}{36}+\frac{31{\mathrm{e}}^t}{25},y\left(t\right)=\frac{19{\mathrm{e}}^{2t}}{36}-{\mathrm{e}}^{-4t}\mathit{\_}\mathit{C}\mathit{2}-{\mathrm{e}}^{-4t}t\mathit{\_}\mathit{C}\mathit{1}-{\mathrm{e}}^{-4t}\mathit{\_}\mathit{C}\mathit{1}-\frac{11{\mathrm{e}}^t}{25}\}\right\}$$