8.118   ODE No. 1708

$$\boxed{{\displaystyle \left(\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)\right)y\left(x\right)-{\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2+ay\left(x\right)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-2a{\left(y\left(x\right)\right)}^2+b{\left(y\left(x\right)\right)}^3=0}}$$

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

Mathematica: cpu = 46.194866 (sec), leaf count = 43 $$\text{DSolve}[ay(x)y^{\prime }(x)-2ay(x{)}^2+by(x{)}^3+y(x)y^{″}(x)-y^{\prime }(x{)}^2=0,y(x),x]$$

Maple: cpu = 2.106 (sec), leaf count = 73 $$\{y\left(x\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}(\mathit{\_}\mathit{a},[\{\left(\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)-\frac{{\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2-\mathit{\_}\mathit{a}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)a-b{\mathit{\_}\mathit{a}}^3+2{\mathit{\_}\mathit{a}}^{2}a}{\mathit{\_}\mathit{a}}=0\},\{\mathit{\_}\mathit{a}=y\left(x\right),\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\},\{x=\int {\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^{-1}\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1},y\left(x\right)=\mathit{\_}\mathit{a}\}])\}$$