8.69   ODE No. 1659

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

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

Mathematica: cpu = 12.591099 (sec), leaf count = 26 $$\text{DSolve}[y^{″}(x)-y(x)h(x,\frac{y^{\prime }(x)}{y(x)})=0,y(x),x]$$

Maple: cpu = 0.063 (sec), leaf count = 60 $$\{y\left(x\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}({\mathrm{e}}^{\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}},[\{\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=-{\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2+h(\mathit{\_}\mathit{a},\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right))\},\{\mathit{\_}\mathit{a}=x,\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=\frac{\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)}{y\left(x\right)}\},\{x=\mathit{\_}\mathit{a},y\left(x\right)={\mathrm{e}}^{\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}}\}])\}$$