8.187   ODE No. 1777

$$\boxed{{\displaystyle \mathit{f}\mathit{0}\left(x\right)y\left(x\right)\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+\mathit{f}\mathit{1}\left(x\right){\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2+\mathit{f}\mathit{2}\left(x\right)y\left(x\right)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+\mathit{f}\mathit{3}\left(x\right){\left(y\left(x\right)\right)}^2=0}}$$

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

Mathematica: cpu = 49.431277 (sec), leaf count = 41 $$\text{DSolve}[\text{f0}(x)y(x)y^{″}(x)+\text{f1}(x)y^{\prime }(x{)}^2+\text{f2}(x)y(x)y^{\prime }(x)+\text{f3}(x)y(x{)}^2=0,y(x),x]$$

Maple: cpu = 0.530 (sec), leaf count = 83 $$\{y\left(x\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}({\mathrm{e}}^{\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}},[\{\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=-\frac{(\mathit{f}\mathit{1}\left(\mathit{\_}\mathit{a}\right)+\mathit{f}\mathit{0}\left(\mathit{\_}\mathit{a}\right)){\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2}{\mathit{f}\mathit{0}\left(\mathit{\_}\mathit{a}\right)}-\frac{\mathit{f}\mathit{2}\left(\mathit{\_}\mathit{a}\right)\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)}{\mathit{f}\mathit{0}\left(\mathit{\_}\mathit{a}\right)}-\frac{\mathit{f}\mathit{3}\left(\mathit{\_}\mathit{a}\right)}{\mathit{f}\mathit{0}\left(\mathit{\_}\mathit{a}\right)}\},\{\mathit{\_}\mathit{a}=x,\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=\frac{\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)}{y\left(x\right)}\},\{x=\mathit{\_}\mathit{a},y\left(x\right)={\mathrm{e}}^{\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}}\}])\}$$