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 = 0.142509 (sec), leaf count = 60

\[\text {Solve}\left [-\frac {1}{2} \log \left (\frac {y(x)^2}{x^2}+\frac {y(x)}{x}+1\right )+\log \left (\frac {y(x)}{x}\right )-\frac {\tan ^{-1}\left (\frac {\frac {2 y(x)}{x}+1}{\sqrt {3}}\right )}{\sqrt {3}}=x+c_1,y(x)\right ]\] Maple : cpu = 0.887 (sec), leaf count = 71

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