8.54   ODE No. 1644

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

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

Mathematica: cpu = 62.318914 (sec), leaf count = 32 $$\text{DSolve}[h(y(x))y^{\prime }(x{)}^2+j(y(x))y^{\prime }(x)+k(y(x))+y^{″}(x)=0,y(x),x]$$

Maple: cpu = 0.374 (sec), leaf count = 59 $$\{y\left(x\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}(\mathit{\_}\mathit{a},[\{\left(\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)+h\left(\mathit{\_}\mathit{a}\right){\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2+j\left(\mathit{\_}\mathit{a}\right)\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)+k\left(\mathit{\_}\mathit{a}\right)=0\},\{\mathit{\_}\mathit{a}=y\left(x\right),\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\},\{x=\int {\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^{-1}\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1},y\left(x\right)=\mathit{\_}\mathit{a}\}])\}$$