8.120   ODE No. 1710

$$\boxed{{\displaystyle \left(\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)\right)y\left(x\right)-{\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2+(-1+ay\left(x\right))\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-y\left(x\right)(1+y\left(x\right))(b^2{\left(y\left(x\right)\right)}^2-a^2)=0}}$$

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

Mathematica: cpu = 104.391256 (sec), leaf count = 55 $$\text{DSolve}[-y(x)(y(x)+1)(b^{2}y(x{)}^2-a^2)+(ay(x)-1)y^{\prime }(x)+y(x)y^{″}(x)-y^{\prime }(x{)}^2=0,y(x),x]$$

Maple: cpu = 4.383 (sec), leaf count = 91 $$\{y\left(x\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}(\mathit{\_}\mathit{a},[\{\left(\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)-\frac{{\mathit{\_}\mathit{a}}^4{b}^2+b^2{\mathit{\_}\mathit{a}}^3-{\mathit{\_}\mathit{a}}^2{a}^2-\mathit{\_}\mathit{a}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)a-\mathit{\_}\mathit{a}{a}^2+{\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2+\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)}{\mathit{\_}\mathit{a}}=0\},\{\mathit{\_}\mathit{a}=y\left(x\right),\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\},\{x=\int {\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^{-1}\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1},y\left(x\right)=\mathit{\_}\mathit{a}\}])\}$$