8.131   ODE No. 1721

$$\boxed{{\displaystyle \left(\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)\right)y\left(x\right)-\frac{(a-1){\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2}{a}-f\left(x\right){\left(y\left(x\right)\right)}^2\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+\frac{a{\left(f\left(x\right)\right)}^2{\left(y\left(x\right)\right)}^4}{{(a+2)}^2}-\frac{a\left(\frac{\mathrm{d}}{\mathrm{d}x}f\left(x\right)\right){\left(y\left(x\right)\right)}^3}{a+2}=0}}$$

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

Mathematica: cpu = 0.927618 (sec), leaf count = 71 $$\text{DSolve}[-\frac{ay(x{)}^3{f}^{\prime }(x)}{a+2}+\frac{af(x{)}^{2}y(x{)}^4}{(a+2{)}^2}-\frac{(a-1)y^{\prime }(x{)}^2}{a}-f(x)y(x{)}^2{y}^{\prime }(x)+y(x)y^{″}(x)=0,y(x),x]$$

Maple: cpu = 1.856 (sec), leaf count = 0 $$\text{could not solve}$$