2.1868   ODE No. 1868

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

$$\{x^{\prime }(t)+3x(t)-y(t)=e^{2t},x(t)+y^{\prime }(t)+5y(t)=e^t\}$$ ✓ Mathematica : cpu = 0.0777104 (sec), leaf count = 162

$$\left\{\{x(t)\to -e^t(t+1)(\frac{t}{5}+\frac{1}{36}{e}^t(6t-7)-\frac{1}{25})+e^{t}t(\frac{t}{5}+\frac{1}{36}{e}^t(6t-1)+\frac{4}{25})+c_1{e}^{-4t}(t+1)+c_2{e}^{-4t}t,y(t)\to e^{t}t(\frac{t}{5}+\frac{1}{36}{e}^t(6t-7)-\frac{1}{25})-e^t(t-1)(\frac{t}{5}+\frac{1}{36}{e}^t(6t-1)+\frac{4}{25})-c_1{e}^{-4t}t-c_2{e}^{-4t}(t-1)\}\right\}$$ ✓ Maple : cpu = 0.116 (sec), leaf count = 64

$$\left\{\{x\left(t\right)={\mathrm{e}}^{-4t}\mathit{\_}\mathit{C}\mathit{2}+{\mathrm{e}}^{-4t}t\mathit{\_}\mathit{C}\mathit{1}+\frac{{\mathrm{e}}^t}{25}+\frac{7{\mathrm{e}}^{2t}}{36},y\left(t\right)=-\frac{{\mathrm{e}}^{2t}}{36}-{\mathrm{e}}^{-4t}\mathit{\_}\mathit{C}\mathit{2}-{\mathrm{e}}^{-4t}t\mathit{\_}\mathit{C}\mathit{1}+{\mathrm{e}}^{-4t}\mathit{\_}\mathit{C}\mathit{1}+\frac{4{\mathrm{e}}^t}{25}\}\right\}$$