Question

The solution of the differential equation $x \sec y \frac { d y } { d x } = 1$ is

• A. $x \sec y \tan y = c$
• B. $c x = \sec y + \tan y$
• C. $c y = \sec x \tan x$
• D. $c y = \sec x + \tan x$

Answer 1

Answer: (B)

$c x = \sec y + \tan y$

Answer 2

$x \sec y \frac { d y } { d x } = 1$ ⇒ $\sec y d y = \frac { d x } { x }$

On integrating both sides, we get

$\log ( \sec y + \tan y ) = \log x + \log c$⇒ $\sec y + \tan y = c x$.