3.574   ODE No. 574

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

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

Mathematica: cpu = 0.014502 (sec), leaf count = 102 $$\left\{\{y(x)\to \frac{1}{9}(9f\left(c_1\right)+2\sqrt{6}x\sqrt{x-c_1}-2\sqrt{6}{c}_1\sqrt{x-c_1}),y(x)\to \frac{1}{9}(9f\left(c_1\right)-2\sqrt{6}x\sqrt{x-c_1}+2\sqrt{6}{c}_1\sqrt{x-c_1})\}\right\}$$

Maple: cpu = 0.109 (sec), leaf count = 67 $$\{y\left(x\right)=f\left(\mathit{\_}\mathit{C}\mathit{1}\right)-\frac{2}{9}\sqrt{-6{\mathit{\_}\mathit{C}\mathit{1}}^3+18{\mathit{\_}\mathit{C}\mathit{1}}^{2}x-18x^2\mathit{\_}\mathit{C}\mathit{1}+6x^3},y\left(x\right)=f\left(\mathit{\_}\mathit{C}\mathit{1}\right)+\frac{2}{9}\sqrt{-6{\mathit{\_}\mathit{C}\mathit{1}}^3+18{\mathit{\_}\mathit{C}\mathit{1}}^{2}x-18x^2\mathit{\_}\mathit{C}\mathit{1}+6x^3}\}$$