3.320   ODE No. 320

\[ \boxed { \left ( {x}^{2} \left ( y \left ( x \right ) \right ) ^{3}+xy \left ( x \right ) \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -1=0} \]

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

Mathematica: cpu = 0.057007 (sec), leaf count = 76 \[ \left \{\left \{y(x)\to -\frac {\sqrt {2 x W\left (c_1 e^{\frac {1}{2 x}-1}\right )+2 x-1}}{\sqrt {x}}\right \},\left \{y(x)\to \frac {\sqrt {2 x W\left (c_1 e^{\frac {1}{2 x}-1}\right )+2 x-1}}{\sqrt {x}}\right \}\right \} \]

Maple: cpu = 0.078 (sec), leaf count = 70 \[ \left \{ y \left ( x \right ) ={\frac {1}{x}\sqrt {x \left ( 2\,{\it lambertW} \left ( 1/2\,{\it \_C1}\,{{\rm e}^{-1/2\,{\frac {2\,x-1}{x}}} } \right ) x+2\,x-1 \right ) }},y \left ( x \right ) =-{\frac {1}{x}\sqrt {x \left ( 2\,{\it lambertW} \left ( 1/2\,{\it \_C1}\,{{\rm e}^{-1/2\,{ \frac {2\,x-1}{x}}}} \right ) x+2\,x-1 \right ) }} \right \} \]