3.255   ODE No. 255

\[ \boxed { x \left ( xy \left ( x \right ) -3 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +x \left ( y \left ( x \right ) \right ) ^{2}-y \left ( x \right ) =0} \]

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

Mathematica: cpu = 5.161155 (sec), leaf count = 31 \[ \left \{\left \{y(x)\to -\frac {3 W\left (2 e^{\frac {9 c_1}{2^{2/3}}-1} x^{2/3}\right )}{x}\right \}\right \} \]

Maple: cpu = 0.156 (sec), leaf count = 74 \[ \left \{ y \left ( x \right ) =-3\,{\frac {{\it lambertW} \left ( 2/3\, \sqrt [3]{-1/8\,{x}^{2}}{\it \_C1} \right ) }{x}},y \left ( x \right ) =- 3\,{\frac {{\it lambertW} \left ( 1/3\,\sqrt [3]{-1/8\,{x}^{2}}{\it \_C1}\, \left ( i\sqrt {3}-1 \right ) \right ) }{x}},y \left ( x \right ) =-3\,{\frac {{\it lambertW} \left ( -1/3\,\sqrt [3]{-1/8\,{x}^{2}}{\it \_C1}\, \left ( i\sqrt {3}+1 \right ) \right ) }{x}} \right \} \]