8.114   ODE No. 1704

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

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

Mathematica: cpu = 41.261240 (sec), leaf count = 62 $$\text{DSolve}[y(x{)}^2(\frac{f^{″}(x)}{f(x)}-\frac{f^{\prime }(x{)}^2}{f(x{)}^2})+f(x)y(x{)}^3+y(x)y^{″}(x)-y^{\prime }(x{)}^2-y^{\prime }(x)=0,y(x),x]$$

Maple: cpu = 0.390 (sec), leaf count = 0 $$\text{could not solve}$$