The particular solution of the differential equation $\cos \left(\frac{d y}{d x}\right)=a,(a \in R) ; y=2$ at x = 0 is given by

$\cos \left(\frac{y-2}{x}\right)=a$ $\cos \left(\frac{y-a}{x}\right)=2$ $-\sin \left(\frac{y-2}{x}\right)=a$ $-\sin \left(\frac{y-a}{x}\right)=2$

$\cos \left(\frac{y-2}{x}\right)=a$

The correct answer is Option (1) → $\cos \left(\frac{y-2}{x}\right)=a$