2.254   ODE No. 254

\[ x^2 y(x)^3+x (x y(x)-2) y'(x)+x y(x)^2-2 y(x)=0 \] Mathematica : cpu = 0.13917 (sec), leaf count = 99


\[\left \{\left \{y(x)\to -\frac {2 x}{-x^2+\frac {\sqrt {2} \sqrt {-\frac {x}{2}-2 x (-\log (x)+c_1)}}{\sqrt {-\frac {1}{x^3}}}}\right \},\left \{y(x)\to \frac {2 x}{x^2+\frac {\sqrt {2} \sqrt {-\frac {x}{2}-2 x (-\log (x)+c_1)}}{\sqrt {-\frac {1}{x^3}}}}\right \}\right \}\] Maple : cpu = 0.027 (sec), leaf count = 59


\[y \relax (x ) = \frac {-1+\sqrt {1-4 \ln \relax (x )+4 c_{1}}}{2 \left (-\ln \relax (x )+c_{1}\right ) x}\]