ODE No. 301

\[ \left (x^2+6 x y(x)^2\right ) y'(x)-y(x) \left (3 y(x)^2-x\right )=0 \] Mathematica : cpu = 0.14042 (sec), leaf count = 64

DSolve[-(y[x]*(-x + 3*y[x]^2)) + (x^2 + 6*x*y[x]^2)*Derivative[1][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to -\frac {\sqrt {x} \sqrt {W\left (\frac {6 e^{3 c_1}}{x^3}\right )}}{\sqrt {6}}\right \},\left \{y(x)\to \frac {\sqrt {x} \sqrt {W\left (\frac {6 e^{3 c_1}}{x^3}\right )}}{\sqrt {6}}\right \}\right \}\] Maple : cpu = 0.202 (sec), leaf count = 25

dsolve((6*x*y(x)^2+x^2)*diff(y(x),x)-y(x)*(3*y(x)^2-x) = 0,y(x))
 

\[y \left (x \right ) = \frac {{\mathrm e}^{-\frac {\LambertW \left (\frac {6 \,{\mathrm e}^{3 c_{1}}}{x^{3}}\right )}{2}+\frac {3 c_{1}}{2}}}{x}\]