2.978   ODE No. 978

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

\[ y'(x)=\frac {y(x) \left (x^2+x y(x)+y(x)^2+x\right )}{x^2} \] Mathematica : cpu = 0.188581 (sec), leaf count = 58

\[\text {Solve}\left [\log \left (\frac {y(x)}{x}\right )=c_1+\frac {1}{2} \log \left (\frac {x^2+x y(x)+y(x)^2}{x^2}\right )+\frac {\tan ^{-1}\left (\frac {2 y(x)+x}{\sqrt {3} x}\right )}{\sqrt {3}}+x,y(x)\right ]\]

Maple : cpu = 0.191 (sec), leaf count = 71

\[ \left \{ y \left ( x \right ) =-{\frac {x}{2}}+{\frac {\sqrt {3}x}{2}\tan \left ( {\it RootOf} \left ( -\sqrt {3}\ln \left ( 3 \right ) -\sqrt {3}\ln \left ( {\frac {4}{3+3\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}}} \right ) -2\,\sqrt {3}\ln \left ( -1/6\,\sqrt {3}+1/2\,\tan \left ( {\it \_Z} \right ) \right ) +2\,\sqrt {3}{\it \_C1}+2\,\sqrt {3}x+2\,{\it \_Z} \right ) \right ) } \right \} \]