Question

What is the equation of a curve passing through (0, 1) and whose differential equation is given by dy = y tan x dx ?

• A. y = cos x
• B. y = sin x
• C. y = sec x
• D. y = cosec x

Answer 1

The correct option is C y = sec x

Given : $dy=y\tan xdx$

$\frac{dy}{y}=\tan xdx$

On integrating both sides, we get

$\Rightarrow \ln y=-\ln \cos x+c$

The equation satisfies $(0,1)$

$\Rightarrow 0=0+c$

$\Rightarrow c=0$

We get

$y=\frac{1}{\cos x}$

$y=\sec x$