Let \(y=y(x)\) be the solution of the differential equation \(x\sqrt{1-{x}^{2}}dy+\left(y\sqrt{1-{x}^{2}}-x{\cos }^{-1}x…

Let \(y=y(x)\) be the solution of the differential equation \(x\sqrt{1-{x}^{2}}dy+\left(y\sqrt{1-{x}^{2}}-x{\cos }^{-1}x\right)dx=0\), \(x\in \left(0,1\right)\), \(\lim _{x\to {1}^{-}}y\left(x\right)=1\). Then \(y\left(\frac{1}{2}\right)\) equals:

[JEE Main 2026, 8 Apr (Shift 2)]