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 = 3.27877 (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 = 0.179 (sec), leaf count = 74

\[ \left \{ y \left ( x \right ) =-3\,{\frac {{\it lambertW} \left ( 2/3\,\sqrt [3]{-1/8\,{x}^{2}}{\it \_C1} \right ) }{x}},y \left ( x \right ) =-3\,{\frac {{\it lambertW} \left ( 1/3\,\sqrt [3]{-1/8\,{x}^{2}}{\it \_C1}\, \left ( -1+i\sqrt {3} \right ) \right ) }{x}},y \left ( x \right ) =-3\,{\frac {{\it lambertW} \left ( -1/3\,\sqrt [3]{-1/8\,{x}^{2}}{\it \_C1}\, \left ( 1+i\sqrt {3} \right ) \right ) }{x}} \right \} \]