8.225   ODE No. 1815

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

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

Mathematica: cpu = 1.169649 (sec), leaf count = 45 $$\text{DSolve}[h(y(x){)}^2(-j(x,\frac{y^{\prime }(x)}{h(y(x))}))+h(y(x))y^{″}(x)-h(y(x))y^{\prime }(x{)}^2=0,y(x),x]$$

Maple: cpu = 0.780 (sec), leaf count = 74 $$\{y\left(x\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}-{\int }^{\mathit{\_}\mathit{Z}}{\left(h\left(\mathit{\_}\mathit{f}\right)\right)}^{-1}d\mathit{\_}\mathit{f}),[\{\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=j(\mathit{\_}\mathit{a},\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right))\},\{\mathit{\_}\mathit{a}=x,\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=\frac{\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)}{h\left(y\left(x\right)\right)}\},\{x=\mathit{\_}\mathit{a},y\left(x\right)=\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}-{\int }^{\mathit{\_}\mathit{Z}}{\left(h\left(\mathit{\_}\mathit{f}\right)\right)}^{-1}d\mathit{\_}\mathit{f})\}])\}$$