2.768   ODE No. 768

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

\[ y'(x)=\frac {y(x) (y(x)+1)}{x (x y(x)-y(x)-1)} \] Mathematica : cpu = 1.79393 (sec), leaf count = 66

\[\text {Solve}\left [\frac {2^{2/3} \left (x y(x) \left (-\log \left (\frac {x y(x)}{(x-1) y(x)-1}\right )+\log \left (\frac {y(x)+1}{-x y(x)+y(x)+1}\right )+\log (x)+1\right )-1\right )}{9 x y(x)}=c_1,y(x)\right ]\] Maple : cpu = 0.129 (sec), leaf count = 26

\[\left \{y \left (x \right ) = -\frac {1}{x \LambertW \left (\frac {{\mathrm e}^{-\frac {1}{x}}}{c_{1} x}\right )+1}\right \}\]