8.33   ODE No. 1623

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

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

Mathematica: cpu = 0.445557 (sec), leaf count = 50 $$\text{DSolve}[y(x)(f^{\prime }(x)+2f(x{)}^2)+(3f(x)+y(x))y^{\prime }(x)+f(x)y(x{)}^2+y^{″}(x)-y(x{)}^3=0,y(x),x]$$

Maple: cpu = 2.340 (sec), leaf count = 0 $$\text{could not solve}$$