10.15   ODE No. 1870

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

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

Mathematica: cpu = 0.127016 (sec), leaf count = 122 $$\left\{\{x(t)\to -\frac{3}{4}{c}_2(e^{4t}-1)+c_1+\frac{1}{68}{e}^{-4t}(e^{4t}-1)(34e^t+3\sin (t)-12\cos (t))+\frac{1}{4}(2e^{-3t}+2e^t+\frac{3}{17}{e}^{-4t}\sin (t)+\sin (t)-\frac{12}{17}{e}^{-4t}\cos (t)),y(t)\to c_2{e}^{4t}+\frac{1}{51}(-34e^t-3\sin (t)+12\cos (t))\}\right\}$$

Maple: cpu = 0.078 (sec), leaf count = 47 $$\left\{\{x\left(t\right)={\mathrm{e}}^t+\frac{5\sin \left(t\right)}{17}-\frac{3\cos \left(t\right)}{17}+\frac{{\mathrm{e}}^{4t}\mathit{\_}\mathit{C}\mathit{1}}{4}+\mathit{\_}\mathit{C}\mathit{2},y\left(t\right)=-\frac{2{\mathrm{e}}^t}{3}+\frac{4\cos \left(t\right)}{17}-\frac{\sin \left(t\right)}{17}-\frac{{\mathrm{e}}^{4t}\mathit{\_}\mathit{C}\mathit{1}}{3}\}\right\}$$