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

DSolve[-(x*y[x]) + (x^2 + 4*y[x]^2)*Derivative[1][y][x] == 0,y[x],x]
 

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

dsolve((4*y(x)^2+x^2)*diff(y(x),x)-x*y(x) = 0,y(x))
 

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