2.320   ODE No. 320

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

\[ \left (x^2 y(x)^3+x y(x)\right ) y'(x)-1=0 \] Mathematica : cpu = 0.116521 (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 = 0.073 (sec), leaf count = 78

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