8.35   ODE No. 1625

$$\boxed{{\displaystyle \frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+(y\left(x\right)-3/2\frac{\frac{\mathrm{d}}{\mathrm{d}x}f\left(x\right)}{f\left(x\right)})\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-{\left(y\left(x\right)\right)}^3-1/2\frac{\left(\frac{\mathrm{d}}{\mathrm{d}x}f\left(x\right)\right){\left(y\left(x\right)\right)}^2}{f\left(x\right)}+1/2\frac{y\left(x\right)}{f\left(x\right)}(f\left(x\right)+\frac{{\left(\frac{\mathrm{d}}{\mathrm{d}x}f\left(x\right)\right)}^2}{{\left(f\left(x\right)\right)}^2}-\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}f\left(x\right))=0}}$$

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

Mathematica: cpu = 0.963122 (sec), leaf count = 82 $$\text{DSolve}[y^{\prime }(x)(y(x)-\frac{3f^{\prime }(x)}{2f(x)})-\frac{y(x{)}^2{f}^{\prime }(x)}{2f(x)}+y(x)(-\frac{f^{″}(x)}{2f(x)}+\frac{f^{\prime }(x{)}^2}{f(x{)}^2}+f(x))+y^{″}(x)-y(x{)}^3=0,y(x),x]$$

Maple: cpu = 0.343 (sec), leaf count = 0 $$\text{could not solve}$$