2.272   ODE No. 272

\[ \left (x^2+y(x)^2\right ) y'(x)-y(x)^2=0 \] Mathematica : cpu = 0.154072 (sec), leaf count = 42


\[\text {Solve}\left [\log \left (\frac {y(x)}{x}\right )+\frac {2 \tan ^{-1}\left (\frac {\frac {2 y(x)}{x}-1}{\sqrt {3}}\right )}{\sqrt {3}}=-\log (x)+c_1,y(x)\right ]\] Maple : cpu = 0.149 (sec), leaf count = 43


\[y \relax (x ) = {\mathrm e}^{\frac {2 \sqrt {3}\, \RootOf \left (-\sqrt {3}\, x \,{\mathrm e}^{c_{1}}+3 \tan \left (\textit {\_Z} \right ) x \,{\mathrm e}^{c_{1}}+2 \sqrt {3}\, {\mathrm e}^{\frac {2 \sqrt {3}\, \textit {\_Z}}{3}}\right )}{3}-c_{1}}\]