Question

What is the solution of the differential equation $\sin \left(\frac{dy}{dx}\right)-a=0$?
where $c$ is an arbitrary constant.

• A. $y=x{\sin }^{-1}a+c$
• B. $x=y{\sin }^{-1}a+c$
• C. $y=x+x{\sin }^{-1}a+c$
• D. $y={\sin }^{-1}a+c$

Answer 1

The correct option is A $y=x{\sin }^{-1}a+c$

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

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

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

Integrating both the sides, we get

$\int dy=\int {\sin }^{-1}adx$

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

where $c$ is a constant.