10.16   ODE No. 1871

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

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

Mathematica: cpu = 0.161521 (sec), leaf count = 180 $$\left\{\{x(t)\to -c_2{e}^{-4t}\sin (t)+c_1{e}^{-4t}(\cos (t)-\sin (t))+\frac{1}{442}(3(153e^t-754)\sin (t)+31(17e^t-78)\cos (t))(\cos (t)-\sin (t))+\frac{1}{221}\sin (t)((493e^t-2340)\sin (t)+(34e^t-78)\cos (t)),y(t)\to 2c_1{e}^{-4t}\sin (t)+c_2{e}^{-4t}(\sin (t)+\cos (t))+\frac{1}{221}\sin (t)(3(153e^t-754)\sin (t)+31(17e^t-78)\cos (t))-\frac{1}{221}(\sin (t)+\cos (t))((493e^t-2340)\sin (t)+(34e^t-78)\cos (t))\}\right\}$$

Maple: cpu = 0.047 (sec), leaf count = 71 $$\left\{\{x\left(t\right)={\mathrm{e}}^{-4t}\sin \left(t\right)\mathit{\_}\mathit{C}\mathit{2}+{\mathrm{e}}^{-4t}\cos \left(t\right)\mathit{\_}\mathit{C}\mathit{1}-\frac{93}{17}+\frac{31{\mathrm{e}}^t}{26},y\left(t\right)=-{\mathrm{e}}^{-4t}\sin \left(t\right)\mathit{\_}\mathit{C}\mathit{2}-{\mathrm{e}}^{-4t}\cos \left(t\right)\mathit{\_}\mathit{C}\mathit{2}-{\mathrm{e}}^{-4t}\cos \left(t\right)\mathit{\_}\mathit{C}\mathit{1}+{\mathrm{e}}^{-4t}\sin \left(t\right)\mathit{\_}\mathit{C}\mathit{1}-\frac{2{\mathrm{e}}^t}{13}+\frac{6}{17}\}\right\}$$