8.129   ODE No. 1719

$$\boxed{{\displaystyle \left(\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)\right)y\left(x\right)+a{\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2+f\left(x\right)y\left(x\right)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+g\left(x\right){\left(y\left(x\right)\right)}^2=0}}$$

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

Mathematica: cpu = 41.860316 (sec), leaf count = 38 $$\text{DSolve}[a{y}^{\prime }(x{)}^2+f(x)y(x)y^{\prime }(x)+g(x)y(x{)}^2+y(x)y^{″}(x)=0,y(x),x]$$

Maple: cpu = 0.374 (sec), leaf count = 70 $$\{y\left(x\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}({\mathrm{e}}^{\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}},[\{\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=(-a-1){\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2-f\left(\mathit{\_}\mathit{a}\right)\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)-g\left(\mathit{\_}\mathit{a}\right)\},\{\mathit{\_}\mathit{a}=x,\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=\frac{\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)}{y\left(x\right)}\},\{x=\mathit{\_}\mathit{a},y\left(x\right)={\mathrm{e}}^{\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}}\}])\}$$