\[ \sqrt {1-x^2} y'(x)-y(x) \sqrt {y(x)^2-1}=0 \] ✓ Mathematica : cpu = 0.122627 (sec), leaf count = 79
DSolve[-(y[x]*Sqrt[-1 + y[x]^2]) + Sqrt[1 - x^2]*Derivative[1][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to -\sqrt {1+\tan ^2\left (2 \arctan \left (\frac {\sqrt {1-x^2}}{x+1}\right )-c_1\right )}\right \},\left \{y(x)\to \sqrt {1+\tan ^2\left (2 \arctan \left (\frac {\sqrt {1-x^2}}{x+1}\right )-c_1\right )}\right \}\right \}\] ✓ Maple : cpu = 0.012 (sec), leaf count = 16
dsolve((-x^2+1)^(1/2)*diff(y(x),x)-y(x)*(y(x)^2-1)^(1/2) = 0,y(x))
\[\arcsin \left (x \right )+\arctan \left (\frac {1}{\sqrt {y \left (x \right )^{2}-1}}\right )+c_{1} = 0\]