3.272   ODE No. 272

\[ \boxed { \left ( \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2} \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) - \left ( y \left ( x \right ) \right ) ^{2}=0} \]

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

Mathematica: cpu = 0.044506 (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 = 0.109 (sec), leaf count = 43 \[ \left \{ y \left ( x \right ) ={{\rm e}^{{\frac {2\,\sqrt {3}}{3}{\it RootOf} \left ( -\sqrt {3}x{{\rm e}^{{\it \_C1}}}+3\,\tan \left ( {\it \_Z} \right ) x{{\rm e}^{{\it \_C1}}}+2\,\sqrt {3}{{\rm e}^{2/3\,\sqrt {3}{\it \_Z}}} \right ) }-{\it \_C1}}} \right \} \]