2.255   ODE No. 255

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

\[ x (x y(x)-3) y'(x)+x y(x)^2-y(x)=0 \] Mathematica : cpu = 6.01949 (sec), leaf count = 30

\[\left \{\left \{y(x)\to -\frac {3 W\left (e^{-1+\frac {9 c_1}{2^{2/3}}} x^{2/3}\right )}{x}\right \}\right \}\] Maple : cpu = 0.214 (sec), leaf count = 74

\[\left \{y \left (x \right ) = -\frac {3 \LambertW \left (\frac {2 c_{1} \left (-\frac {x^{2}}{8}\right )^{\frac {1}{3}}}{3}\right )}{x}, y \left (x \right ) = -\frac {3 \LambertW \left (-\frac {c_{1} \left (-\frac {x^{2}}{8}\right )^{\frac {1}{3}} \left (1+i \sqrt {3}\right )}{3}\right )}{x}, y \left (x \right ) = -\frac {3 \LambertW \left (\frac {c_{1} \left (-\frac {x^{2}}{8}\right )^{\frac {1}{3}} \left (i \sqrt {3}-1\right )}{3}\right )}{x}\right \}\]