\[ y(x) \left (x^2 y(x)^2+1\right )+x (x y(x)-1)^2 y'(x)=0 \] ✓ Mathematica : cpu = 0.147247 (sec), leaf count = 25
DSolve[y[x]*(1 + x^2*y[x]^2) + x*(-1 + x*y[x])^2*Derivative[1][y][x] == 0,y[x],x]
\[\text {Solve}\left [x y(x)-\frac {1}{x y(x)}-2 \log (y(x))=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.235 (sec), leaf count = 34
dsolve((x*y(x)-1)^2*x*diff(y(x),x)+(x^2*y(x)^2+1)*y(x) = 0,y(x))
\[y \left (x \right ) = \frac {{\mathrm e}^{\RootOf \left (-{\mathrm e}^{2 \textit {\_Z}}-2 \,{\mathrm e}^{\textit {\_Z}} \ln \left (x \right )+2 \,{\mathrm e}^{\textit {\_Z}} c_{1}+2 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+1\right )}}{x}\]