8.37   ODE No. 1627

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

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

Mathematica: cpu = 0.325541 (sec), leaf count = 35 $$\text{DSolve}[f(x)(y^{\prime }(x)+y(x{)}^2)-g(x)+y^{″}(x)+2y(x)y^{\prime }(x)=0,y(x),x]$$

Maple: cpu = 0.609 (sec), leaf count = 63 $$\{y\left(x\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right),[\{{\mathrm{e}}^{\int f\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}}{\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2+{\mathrm{e}}^{\int f\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}}\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)-\int {\mathrm{e}}^{\int f\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}}g\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}=0\},\{\mathit{\_}\mathit{a}=x,\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=y\left(x\right)\},\{x=\mathit{\_}\mathit{a},y\left(x\right)=\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\}])\}$$