Question

$\cos \left(\frac{dy}{dx}\right)=a(a\in R);y=1$ when $x=0$.Find $y$?

Answer 1

Given $\cos (\frac{dy}{dx})=a$

$⟹\frac{dy}{dx}={\text{cos}}^{-1}a$

$⟹dy={\text{cos}}^{-1}adx$

Integrating on both sides

$y=x{\text{cos}}^{-1}a+C$

Given $y=1$ when $x=0$

$⟹1=0+C⟹C=1$

So $y=x{\text{cos}}^{-1}a+1$