\[ \left (x^2-1\right ) y'(x)^2-y(x)^2+1=0 \] ✓ Mathematica : cpu = 0.06461 (sec), leaf count = 349
DSolve[1 - y[x]^2 + (-1 + x^2)*Derivative[1][y][x]^2 == 0,y[x],x]
\[\left \{\left \{y(x)\to -\frac {1}{2} e^{-c_1} \sqrt {2 x^2+2 e^{4 c_1} x^2-2 \sqrt {(x-1) (x+1)} x+2 e^{4 c_1} \sqrt {(x-1) (x+1)} x-1+2 e^{2 c_1}-e^{4 c_1}}\right \},\left \{y(x)\to \frac {1}{2} e^{-c_1} \sqrt {2 x^2+2 e^{4 c_1} x^2-2 \sqrt {(x-1) (x+1)} x+2 e^{4 c_1} \sqrt {(x-1) (x+1)} x-1+2 e^{2 c_1}-e^{4 c_1}}\right \},\left \{y(x)\to -\frac {1}{2} \sqrt {2 e^{-2 c_1} x^2+2 e^{2 c_1} x^2+2 e^{-2 c_1} \sqrt {x^2-1} x-2 e^{2 c_1} \sqrt {x^2-1} x+2-e^{-2 c_1}-e^{2 c_1}}\right \},\left \{y(x)\to \frac {1}{2} \sqrt {2 e^{-2 c_1} x^2+2 e^{2 c_1} x^2+2 e^{-2 c_1} \sqrt {x^2-1} x-2 e^{2 c_1} \sqrt {x^2-1} x+2-e^{-2 c_1}-e^{2 c_1}}\right \}\right \}\] ✓ Maple : cpu = 10.39 (sec), leaf count = 166
dsolve((x^2-1)*diff(y(x),x)^2-y(x)^2+1 = 0,y(x))
\[y \left (x \right ) = -1\]