3.853   ODE No. 853

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=\frac{14xy\left(x\right)+12+2x+x^3{\left(y\left(x\right)\right)}^3+6x^2{\left(y\left(x\right)\right)}^2}{x^2(xy\left(x\right)+2+x)}=0}}$$

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

Mathematica: cpu = 0.016502 (sec), leaf count = 76 $$\{\{y(x)\to \frac{1}{x^3(\frac{1}{x^3}-\frac{1}{x^3\sqrt{c_1-2x}})}-\frac{x+2}{x}\},\{y(x)\to \frac{1}{x^3(\frac{1}{x^3\sqrt{c_1-2x}}+\frac{1}{x^3})}-\frac{x+2}{x}\}\}$$

Maple: cpu = 0.031 (sec), leaf count = 65 $$\{y\left(x\right)=-\frac{1}{x}(2\sqrt{\mathit{\_}\mathit{C}\mathit{1}-2x}-x-2){(\sqrt{\mathit{\_}\mathit{C}\mathit{1}-2x}-1)}^{-1},y\left(x\right)=-\frac{1}{x}(2\sqrt{\mathit{\_}\mathit{C}\mathit{1}-2x}+x+2){(\sqrt{\mathit{\_}\mathit{C}\mathit{1}-2x}+1)}^{-1}\}$$