3.301   ODE No. 301

\[ \boxed { \left ( 6\,x \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2} \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -y \left ( x \right ) \left ( 3\, \left ( y \left ( x \right ) \right ) ^{2}-x \right ) =0} \]

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

Mathematica: cpu = 0.039005 (sec), leaf count = 64 \[ \left \{\left \{y(x)\to -\frac {\sqrt {x} \sqrt {W\left (\frac {6 e^{3 c_1}}{x^3}\right )}}{\sqrt {6}}\right \},\left \{y(x)\to \frac {\sqrt {x} \sqrt {W\left (\frac {6 e^{3 c_1}}{x^3}\right )}}{\sqrt {6}}\right \}\right \} \]

Maple: cpu = 0.156 (sec), leaf count = 25 \[ \left \{ y \left ( x \right ) ={\frac {1}{x}{{\rm e}^{-{\frac {1}{2}{ \it lambertW} \left ( 6\,{\frac {{{\rm e}^{3\,{\it \_C1}}}}{{x}^{3}}} \right ) }+{\frac {3\,{\it \_C1}}{2}}}}} \right \} \]