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