2.853   ODE No. 853

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

$$y^{\prime }(x)=\frac{x^{3}y(x{)}^3+6x^{2}y(x{)}^2+14xy(x)+2x+12}{x^2(xy(x)+x+2)}$$ ✓ Mathematica : cpu = 0.214669 (sec), leaf count = 76

$$\{\{y(x)\to -\frac{x+2}{x}+\frac{1}{x^3(\frac{1}{x^3}-\frac{1}{x^3\sqrt{-2x+c_1}})}\},\{y(x)\to -\frac{x+2}{x}+\frac{1}{x^3(\frac{1}{x^3}+\frac{1}{x^3\sqrt{-2x+c_1}})}\}\}$$ ✓ Maple : cpu = 0.12 (sec), leaf count = 63

$$\{y\left(x\right)=\frac{1}{x}(-2\sqrt{\mathit{\_}\mathit{C}\mathit{1}-2x}-x-2){(\sqrt{\mathit{\_}\mathit{C}\mathit{1}-2x}+1)}^{-1},y\left(x\right)=\frac{1}{x}(-2\sqrt{\mathit{\_}\mathit{C}\mathit{1}-2x}+x+2){(\sqrt{\mathit{\_}\mathit{C}\mathit{1}-2x}-1)}^{-1}\}$$