11.2   ODE No. 1914

$$\boxed{{\displaystyle \{\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)=(ay\left(t\right)+b)x\left(t\right),\frac{\mathrm{d}}{\mathrm{d}t}y\left(t\right)=(cx\left(t\right)+d)y\left(t\right)\}}}$$

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

Mathematica: cpu = 0.508065 (sec), leaf count = 201 $$\left\{\{y(t)\to \frac{bW\left(\frac{a\text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}\frac{1}{K[1](W\left(\frac{a{e}^{\frac{cK[1]}{b}+\frac{c_1}{b}}K[1{]}^{\frac{d}{b}}}{b}\right)+1)}dK[1]\mathrm{\&}][bt+c_2]{}^{\frac{d}{b}}\exp (\frac{c\text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}\frac{1}{K[1](W\left(\frac{a{e}^{\frac{cK[1]}{b}+\frac{c_1}{b}}K[1{]}^{\frac{d}{b}}}{b}\right)+1)}dK[1]\mathrm{\&}][bt+c_2]}{b}+\frac{c_1}{b})}{b}\right)}{a},x(t)\to \text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}\frac{1}{K[1](W\left(\frac{a{e}^{\frac{cK[1]}{b}+\frac{c_1}{b}}K[1{]}^{\frac{d}{b}}}{b}\right)+1)}dK[1]\mathrm{\&}][bt+c_2]\}\right\}$$

Maple: cpu = 0.250 (sec), leaf count = 92 $$\{[\{x\left(t\right)=0\},\{y\left(t\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{dt}\}],[\{x\left(t\right)=\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-{\int }^{\mathit{\_}\mathit{Z}}\frac{1}{b\mathit{\_}\mathit{a}}{(\mathit{l}\mathit{a}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathit{t}\mathit{W}\left(\frac{{\mathrm{e}}^{-1}}{b}{\mathrm{e}}^{\frac{c\mathit{\_}\mathit{a}}{b}}{\mathit{\_}\mathit{a}}^{\frac{d}{b}}{\mathrm{e}}^{\frac{\mathit{\_}\mathit{C}\mathit{1}}{b}}\right)+1)}^{-1}d\mathit{\_}\mathit{a}+t+\mathit{\_}\mathit{C}\mathit{2})\},\{y\left(t\right)=\frac{-bx\left(t\right)+\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)}{ax\left(t\right)}\}]\}$$