8.41   ODE No. 1631

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

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

Mathematica: cpu = 0.032004 (sec), leaf count = 35 $$\text{DSolve}[-(f(x)+3y(x))y^{\prime }(x)+f(x)y(x{)}^2+y^{″}(x)+y(x{)}^3=0,y(x),x]$$

Maple: cpu = 0.031 (sec), leaf count = 38 $$\{y\left(x\right)=\frac{-\int \mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{\int f\left(x\right)\mathrm{d}x}\mathrm{d}x-\mathit{\_}\mathit{C}\mathit{2}}{\int \int \mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{\int f\left(x\right)\mathrm{d}x}\mathrm{d}x\mathrm{d}x+\mathit{\_}\mathit{C}\mathit{2}x+1}\}$$