2.255   ODE No. 255

\[ x (x y(x)-3) y'(x)+x y(x)^2-y(x)=0 \] Mathematica : cpu = 6.23949 (sec), leaf count = 30

DSolve[-y[x] + x*y[x]^2 + x*(-3 + x*y[x])*Derivative[1][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to -\frac {3 W\left (e^{-1+\frac {9 c_1}{2^{2/3}}} x^{2/3}\right )}{x}\right \}\right \}\] Maple : cpu = 0.171 (sec), leaf count = 74

dsolve(x*(x*y(x)-3)*diff(y(x),x)+x*y(x)^2-y(x) = 0,y(x))
 

\[y \left (x \right ) = -\frac {3 \operatorname {LambertW}\left (\frac {2 \left (-\frac {x^{2}}{8}\right )^{\frac {1}{3}} c_{1}}{3}\right )}{x}\]