3.248   ODE No. 248

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

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

Mathematica: cpu = 0.013002 (sec), leaf count = 106 $$\{\{y(x)\to -\frac{\sqrt{6c_{1}x-2x^3+\frac{1}{6}{(x^2+3)}^2}}{\sqrt{6}x}-\frac{x^2+3}{6x}\},\{y(x)\to \frac{\sqrt{6c_{1}x-2x^3+\frac{1}{6}{(x^2+3)}^2}}{\sqrt{6}x}-\frac{x^2+3}{6x}\}\}$$

Maple: cpu = 0.016 (sec), leaf count = 71 $$\{y\left(x\right)=\frac{1}{6x}(-x^2-3+\sqrt{x^4-12x^3-12\mathit{\_}\mathit{C}\mathit{1}x+6x^2+9}),y\left(x\right)=-\frac{1}{6x}(x^2+\sqrt{x^4-12x^3-12\mathit{\_}\mathit{C}\mathit{1}x+6x^2+9}+3)\}$$