\[ 2 \left (1-x^2\right ) y(x) y'(x)+x \left (x^2-1\right ) y'(x)^2+x y(x)^2-x=0 \] ✓ Mathematica : cpu = 0.204008 (sec), leaf count = 145
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]
\[\left \{\left \{y(x)\to \frac {x \left (1+\tanh ^2\left (\frac {1}{2} \left (c_1-2 i \arctan \left (\frac {\sqrt {x-1}}{\sqrt {x+1}}\right )\right )\right )\right )}{-1+\tanh ^2\left (\frac {1}{2} \left (c_1-2 i \arctan \left (\frac {\sqrt {x-1}}{\sqrt {x+1}}\right )\right )\right )}\right \},\left \{y(x)\to \frac {x \left (1+\tanh ^2\left (\frac {1}{2} \left (2 i \arctan \left (\frac {\sqrt {x-1}}{\sqrt {x+1}}\right )+c_1\right )\right )\right )}{-1+\tanh ^2\left (\frac {1}{2} \left (2 i \arctan \left (\frac {\sqrt {x-1}}{\sqrt {x+1}}\right )+c_1\right )\right )}\right \}\right \}\] ✓ Maple : cpu = 0.402 (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))
\[y \left (x \right ) = x\]