2.272   ODE No. 272

\[ \left (x^2+y(x)^2\right ) y'(x)-y(x)^2=0 \] Mathematica : cpu = 0.11258 (sec), leaf count = 42

DSolve[-y[x]^2 + (x^2 + y[x]^2)*Derivative[1][y][x] == 0,y[x],x]
 

\[\text {Solve}\left [\frac {2 \arctan \left (\frac {\frac {2 y(x)}{x}-1}{\sqrt {3}}\right )}{\sqrt {3}}+\log \left (\frac {y(x)}{x}\right )=-\log (x)+c_1,y(x)\right ]\] Maple : cpu = 0.111 (sec), leaf count = 42

dsolve((y(x)^2+x^2)*diff(y(x),x)-y(x)^2 = 0,y(x))
 

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