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
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $\cos \left(\frac{y-2}{x}\right)=a$
$\cos\frac{dy}{dx}=a⇒\int\, dy=\cos^{-1}a\int x\,dx$
so $y+c=(\cos^{-1}a)(x)$
at $x=0$, $y=2$
so $c=-2$
$⇒\frac{y-2}{x}=\cos^{-1}a⇒\cos\left(\frac{y-2}{x}\right)=a$