\[ 2 \left (1-x^2\right ) y(x) y'(x)+x \left (x^2-1\right ) y'(x)^2+x y(x)^2-x=0 \] ✓ Mathematica : cpu = 0.128906 (sec), leaf count = 421
DSolve[-x + x*y[x]^2 + 2*(1 - x^2)*y[x]*Derivative[1][y][x] + x*(-1 + x^2)*Derivative[1][y][x]^2 == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {-x-x \tanh ^2\left (\frac {1}{4} \left (-\frac {i \sqrt {x-1} \sqrt {x+1} \sqrt {(x-1) (x+1)} \tan ^{-1}\left (\sqrt {x^2-1}\right )}{1-x}-\frac {i \sqrt {x-1} \sqrt {(x-1) (x+1)} \tan ^{-1}\left (\sqrt {x^2-1}\right )}{\sqrt {x+1}}+2 c_1\right )\right )}{-1+\tanh ^2\left (\frac {1}{4} \left (-\frac {i \sqrt {x-1} \sqrt {x+1} \sqrt {(x-1) (x+1)} \tan ^{-1}\left (\sqrt {x^2-1}\right )}{1-x}-\frac {i \sqrt {x-1} \sqrt {(x-1) (x+1)} \tan ^{-1}\left (\sqrt {x^2-1}\right )}{\sqrt {x+1}}+2 c_1\right )\right )}\right \},\left \{y(x)\to \frac {-x-x \tanh ^2\left (\frac {1}{4} \left (\frac {i \sqrt {x-1} \sqrt {x+1} \sqrt {(x-1) (x+1)} \tan ^{-1}\left (\sqrt {x^2-1}\right )}{1-x}+\frac {i \sqrt {x-1} \sqrt {(x-1) (x+1)} \tan ^{-1}\left (\sqrt {x^2-1}\right )}{\sqrt {x+1}}+2 c_1\right )\right )}{-1+\tanh ^2\left (\frac {1}{4} \left (\frac {i \sqrt {x-1} \sqrt {x+1} \sqrt {(x-1) (x+1)} \tan ^{-1}\left (\sqrt {x^2-1}\right )}{1-x}+\frac {i \sqrt {x-1} \sqrt {(x-1) (x+1)} \tan ^{-1}\left (\sqrt {x^2-1}\right )}{\sqrt {x+1}}+2 c_1\right )\right )}\right \}\right \}\] ✓ Maple : cpu = 0.419 (sec), leaf count = 33
dsolve(x*(x^2-1)*diff(y(x),x)^2+2*(-x^2+1)*y(x)*diff(y(x),x)+x*y(x)^2-x = 0,y(x))
\[y \left (x \right ) = x\]