Question

The particular solution of the differential equation $\frac{dy}{dx}=\sec y,y(0)=0$ is

• A. $x=\cos y$
• B. $x=\sin y+q$
• C. $y=\sin x$
• D. $x=\sin y$

Answer 1

Answer: (D)

Given, differential equation, $\frac{dy}{dx}=\sec y$
$\Rightarrow \int \cos ydy=\int dx$
$\Rightarrow \sin y=x+c$
$\therefore y(0)=0$
$\Rightarrow c=0$
$\therefore$ The required solution of differential equation is $x=\sin y$