8.38   ODE No. 1628

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

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

Mathematica: cpu = 7.278424 (sec), leaf count = 32 $$\text{DSolve}[f(x)y(x)-g(x)+y^{″}(x)+3y(x)y^{\prime }(x)+y(x{)}^3=0,y(x),x]$$

Maple: cpu = 0.0 (sec), leaf count = 63 $$\{y\left(x\right)=\frac{\frac{\mathrm{d}}{\mathrm{d}x}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}(\{-g\left(x\right)\mathit{\_}\mathit{Y}\left(x\right)+f\left(x\right)\frac{\mathrm{d}}{\mathrm{d}x}\mathit{\_}\mathit{Y}\left(x\right)+\frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}\mathit{\_}\mathit{Y}\left(x\right)\},\left\{\mathit{\_}\mathit{Y}\left(x\right)\right\})}{\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}(\{-g\left(x\right)\mathit{\_}\mathit{Y}\left(x\right)+f\left(x\right)\frac{\mathrm{d}}{\mathrm{d}x}\mathit{\_}\mathit{Y}\left(x\right)+\frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}\mathit{\_}\mathit{Y}\left(x\right)\},\left\{\mathit{\_}\mathit{Y}\left(x\right)\right\})}\}$$