2.284   ODE No. 284

\[ \left (x^2+4 y(x)^2\right ) y'(x)-x y(x)=0 \] Mathematica : cpu = 0.111886 (sec), leaf count = 59


\[\left \{\left \{y(x)\to -\frac {x}{2 \sqrt {W\left (\frac {1}{4} e^{-\frac {c_1}{2}} x^2\right )}}\right \},\left \{y(x)\to \frac {x}{2 \sqrt {W\left (\frac {1}{4} e^{-\frac {c_1}{2}} x^2\right )}}\right \}\right \}\] Maple : cpu = 0.116 (sec), leaf count = 21


\[y \relax (x ) = {\mathrm e}^{\frac {\LambertW \left (\frac {{\mathrm e}^{2 c_{1}} x^{2}}{4}\right )}{2}-c_{1}}\]