#### 2.257   ODE No. 257

$x \left (x^4+x y(x)-1\right ) y'(x)-y(x) \left (-x^4+x y(x)-1\right )=0$ Mathematica : cpu = 0.367587 (sec), leaf count = 39

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

$\left \{ y \left ( x \right ) ={\frac {-{\it \_C1}+{{\rm e}^{{\it RootOf} \left ( -2\,{\it \_Z}\,{x}^{4} \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}+2\,{x}^{4} \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}-2\,{{\rm e}^{{\it \_Z}}}{\it \_C1}\,{x}^{4}+ \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}-2\,{{\rm e}^{{\it \_Z}}}{\it \_C1}+{{\it \_C1}}^{2} \right ) }}}{x{{\rm e}^{{\it RootOf} \left ( -2\,{\it \_Z}\,{x}^{4} \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}+2\,{x}^{4} \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}-2\,{{\rm e}^{{\it \_Z}}}{\it \_C1}\,{x}^{4}+ \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}-2\,{{\rm e}^{{\it \_Z}}}{\it \_C1}+{{\it \_C1}}^{2} \right ) }}}} \right \}$