2.320   ODE No. 320

\[ \left (x^2 y(x)^3+x y(x)\right ) y'(x)-1=0 \] Mathematica : cpu = 0.118859 (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 = 0.101 (sec), leaf count = 78


\[y \relax (x ) = \frac {\sqrt {2 x^{2} \LambertW \left (\frac {c_{1} {\mathrm e}^{-\frac {2 x -1}{2 x}}}{2}\right )+2 x^{2}-x}}{x}\]