8.103   ODE No. 1693

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

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

Mathematica: cpu = 0.952121 (sec), leaf count = 39 $$\text{DSolve}[-h(y(x),f(x)y^{\prime }(x))+f(x)f^{\prime }(x)y^{\prime }(x)+f(x{)}^2{y}^{″}(x)=0,y(x),x]$$

Maple: cpu = 0.218 (sec), leaf count = 68 $$\{y\left(x\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}(\mathit{\_}\mathit{a},[\{\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=-h(\mathit{\_}\mathit{a},{\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^{-1}){\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^3\},\{\mathit{\_}\mathit{a}=y\left(x\right),\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=\frac{1}{f\left(x\right)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)}\},\{x=\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}-{\int }^{\mathit{\_}\mathit{Z}}{\left(f\left(\mathit{\_}\mathit{f}\right)\right)}^{-1}d\mathit{\_}\mathit{f}),y\left(x\right)=\mathit{\_}\mathit{a}\}])\}$$