2.257   ODE No. 257

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

$$x(x^4+xy(x)-1)y^{\prime }(x)-y(x)(-x^4+xy(x)-1)=0$$ ✓ Mathematica : cpu = 0.367587 (sec), leaf count = 39

$$\text{Solve}[2x^2+\frac{y(x)}{x}+\frac{x(-2\log \left(\frac{1}{1-xy(x)}\right)-2+c_1)}{y(x)}=0,y(x)]$$ ✓ Maple : cpu = 0.081 (sec), leaf count = 98

$$\{y\left(x\right)=\frac{-\mathit{\_}\mathit{C}\mathit{1}+{\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-2\mathit{\_}\mathit{Z}{x}^4{\left({\mathrm{e}}^{\mathit{\_}\mathit{Z}}\right)}^2+2x^4{\left({\mathrm{e}}^{\mathit{\_}\mathit{Z}}\right)}^2-2{\mathrm{e}}^{\mathit{\_}\mathit{Z}}\mathit{\_}\mathit{C}\mathit{1}{x}^4+{\left({\mathrm{e}}^{\mathit{\_}\mathit{Z}}\right)}^2-2{\mathrm{e}}^{\mathit{\_}\mathit{Z}}\mathit{\_}\mathit{C}\mathit{1}+{\mathit{\_}\mathit{C}\mathit{1}}^2)}}{x{\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-2\mathit{\_}\mathit{Z}{x}^4{\left({\mathrm{e}}^{\mathit{\_}\mathit{Z}}\right)}^2+2x^4{\left({\mathrm{e}}^{\mathit{\_}\mathit{Z}}\right)}^2-2{\mathrm{e}}^{\mathit{\_}\mathit{Z}}\mathit{\_}\mathit{C}\mathit{1}{x}^4+{\left({\mathrm{e}}^{\mathit{\_}\mathit{Z}}\right)}^2-2{\mathrm{e}}^{\mathit{\_}\mathit{Z}}\mathit{\_}\mathit{C}\mathit{1}+{\mathit{\_}\mathit{C}\mathit{1}}^2)}}\}$$