Question

Solve the differential equation $\cos \left(\frac{dy}{dx}\right)=a,(a\in R)$.

Answer 1

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

$\Rightarrow \frac{dy}{dx}={\cos }^{-1}a$

$\Rightarrow dy={\cos }^{-1}adx$

Integrating both the sides,

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