2.260   ODE No. 260

\[ \left (2 x^2 y(x)+x\right ) y'(x)-x^2 y(x)^3+2 x y(x)^2+y(x)=0 \] Mathematica : cpu = 0.130032 (sec), leaf count = 80


\[\left \{\left \{y(x)\to \frac {x}{-2 x^2+\frac {\sqrt {4 x+x (-2 \log (x)+c_1)}}{\sqrt {\frac {1}{x^3}}}}\right \},\left \{y(x)\to -\frac {x}{2 x^2+\frac {\sqrt {4 x+x (-2 \log (x)+c_1)}}{\sqrt {\frac {1}{x^3}}}}\right \}\right \}\] Maple : cpu = 0.03 (sec), leaf count = 59


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