2.295   ODE No. 295

\[ x \left (-x^2+x y(x)+y(x)^2\right ) y'(x)+x^2 y(x)-y(x)^3+x y(x)^2=0 \] Mathematica : cpu = 0.230981 (sec), leaf count = 31


\[\text {Solve}\left [\frac {x}{y(x)}+\frac {y(x)}{x}+\log \left (\frac {y(x)}{x}\right )=-2 \log (x)+c_1,y(x)\right ]\] Maple : cpu = 0.261 (sec), leaf count = 29


\[y \relax (x ) = {\mathrm e}^{\RootOf \left ({\mathrm e}^{2 \textit {\_Z}}+2 \,{\mathrm e}^{\textit {\_Z}} \ln \relax (x )+2 \,{\mathrm e}^{\textit {\_Z}} c_{1}+\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+1\right )} x\]