8.212   ODE No. 1802

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

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

Mathematica: cpu = 0.357545 (sec), leaf count = 41 $$\text{DSolve}[-a{x}^2-bx-c+2y(x{)}^3{y}^{″}(x)+y(x{)}^2{y}^{\prime }(x{)}^2=0,y(x),x]$$

Maple: cpu = 1.903 (sec), leaf count = 0 $$\text{could not solve}$$