2.256   ODE No. 256

\[ x^2 (y(x)-1) y'(x)+(x-1) y(x)=0 \]

✓ Mathematica : cpu = 0.0235343 (sec), leaf count = 21

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

\[\left \{\left \{y(x)\to -W\left (x \left (-e^{\frac {1}{x}-c_1}\right )\right )\right \}\right \}\]

✓ Maple : cpu = 0.208 (sec), leaf count = 31

dsolve(x^2*(-1+y(x))*diff(y(x),x)+(x-1)*y(x) = 0,y(x))
 

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