2.497   ODE No. 497

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

$$-x^2-2xy(x)y^{\prime }(x)+3y(x{)}^2{y}^{\prime }(x{)}^2+4y(x{)}^2=0$$ ✓ Mathematica : cpu = 0.158235 (sec), leaf count = 76

$$\{\{y(x)\to -\frac{\sqrt{-3x^2-4i{e}^{3c_1}x+e^{6c_1}}}{\sqrt{3}}\},\{y(x)\to \frac{\sqrt{-3x^2-4i{e}^{3c_1}x+e^{6c_1}}}{\sqrt{3}}\}\}$$ ✓ Maple : cpu = 0.722 (sec), leaf count = 203

$$\{\ln \left(x\right)-\frac{\sqrt{3}}{6}\sqrt{\frac{(\sqrt{3}x+3y\left(x\right))(\sqrt{3}x-3y\left(x\right))}{x^2}}+\frac{1}{2}\sqrt{\frac{x^2-3{\left(y\left(x\right)\right)}^2}{x^2}}-\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}\left(\frac{1}{2}\sqrt{\frac{x^2-3{\left(y\left(x\right)\right)}^2}{x^2}}\right)+\frac{1}{2}\ln \left(\frac{{\left(y\left(x\right)\right)}^2+x^2}{x^2}\right)-\mathit{\_}\mathit{C}\mathit{1}=0,\ln \left(x\right)+\frac{\sqrt{3}}{6}\sqrt{\frac{(\sqrt{3}x+3y\left(x\right))(\sqrt{3}x-3y\left(x\right))}{x^2}}-\frac{1}{2}\sqrt{\frac{x^2-3{\left(y\left(x\right)\right)}^2}{x^2}}+\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}\left(\frac{1}{2}\sqrt{\frac{x^2-3{\left(y\left(x\right)\right)}^2}{x^2}}\right)+\frac{1}{2}\ln \left(\frac{{\left(y\left(x\right)\right)}^2+x^2}{x^2}\right)-\mathit{\_}\mathit{C}\mathit{1}=0,y\left(x\right)=-\frac{\sqrt{3}x}{3},y\left(x\right)=\frac{\sqrt{3}x}{3}\}$$