11.6   ODE No. 1918

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

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

Mathematica: cpu = 0.090511 (sec), leaf count = 47 $$\text{DSolve}[\{x^{\prime }(t)=-x(t)y(t{)}^2+x(t)+y(t),y^{\prime }(t)=x(t{)}^{2}y(t)-x(t)-y(t)\},\{x(t),y(t)\},t]$$

Maple: cpu = 1.373 (sec), leaf count = 245 $$\{[\{x\left(t\right)=0\},\{y\left(t\right)=0\}],[\{x\left(t\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}(\mathit{\_}\mathit{a},[\{\left(\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)-\frac{1}{2{\mathit{\_}\mathit{a}}^2}(4\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right){\mathit{\_}\mathit{a}}^4-4{\mathit{\_}\mathit{a}}^5+2\mathit{\_}\mathit{a}{\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2-4{\mathit{\_}\mathit{a}}^2\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)+3{\mathit{\_}\mathit{a}}^3-\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)+\mathit{\_}\mathit{a}-\sqrt{-4\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right){\mathit{\_}\mathit{a}}^7+4{\mathit{\_}\mathit{a}}^8+8{\mathit{\_}\mathit{a}}^4{\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2-16{\mathit{\_}\mathit{a}}^5\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)+9{\mathit{\_}\mathit{a}}^6-4{\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^3\mathit{\_}\mathit{a}+12{\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2{\mathit{\_}\mathit{a}}^2-14{\mathit{\_}\mathit{a}}^3\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)+6{\mathit{\_}\mathit{a}}^4+{\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2-2\mathit{\_}\mathit{a}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)+{\mathit{\_}\mathit{a}}^2})=0\},\{\mathit{\_}\mathit{a}=x\left(t\right),\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)\},\{t=\int {\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^{-1}\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1},x\left(t\right)=\mathit{\_}\mathit{a}\}])\},\{y\left(t\right)=\frac{-2{\left(x\left(t\right)\right)}^4+2{\left(x\left(t\right)\right)}^3\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)-\left(\frac{{\mathrm{d}}^2}{\mathrm{d}{t}^2}x\left(t\right)\right)x\left(t\right)+{\left(x\left(t\right)\right)}^2-2x\left(t\right)\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)+{\left(\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)\right)}^2}{-{\left(x\left(t\right)\right)}^3-x\left(t\right)+\frac{\mathrm{d}}{\mathrm{d}t}x\left(t\right)}\}]\}$$