2.301   ODE No. 301

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

\[ \left (x^2+6 x y(x)^2\right ) y'(x)-y(x) \left (3 y(x)^2-x\right )=0 \] Mathematica : cpu = 0.125698 (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 = 0.174 (sec), leaf count = 25

\[ \left \{ y \left ( x \right ) ={\frac {1}{x}{{\rm e}^{-{\frac {1}{2}{\it lambertW} \left ( 6\,{\frac {{{\rm e}^{3\,{\it \_C1}}}}{{x}^{3}}} \right ) }+{\frac {3\,{\it \_C1}}{2}}}}} \right \} \]