ODE No. 272

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

\[ \left (x^2+y(x)^2\right ) y'(x)-y(x)^2=0 \] Mathematica : cpu = 0.122145 (sec), leaf count = 42

\[\text {Solve}\left [\log \left (\frac {y(x)}{x}\right )+\frac {2 \tan ^{-1}\left (\frac {\frac {2 y(x)}{x}-1}{\sqrt {3}}\right )}{\sqrt {3}}=c_1-\log (x),y(x)\right ]\] Maple : cpu = 0.182 (sec), leaf count = 43

\[ \left \{ y \left ( x \right ) ={{\rm e}^{{\frac {2\,\sqrt {3}}{3}{\it RootOf} \left ( -\sqrt {3}x{{\rm e}^{{\it \_C1}}}+3\,\tan \left ( {\it \_Z} \right ) x{{\rm e}^{{\it \_C1}}}+2\,\sqrt {3}{{\rm e}^{2/3\,\sqrt {3}{\it \_Z}}} \right ) }-{\it \_C1}}} \right \} \]