Question

Solve the differential equation:

$\frac{dy}{dx}-y\tan x=0$

Answer 1

Given the differential equation,

$\frac{dy}{dx}-y\tan x=0$

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

Now integrating we have,

$\log |y|=-\log |\cos x|+\log |c|$ [ Where $c$ is integrating constant]

or, $\log |y\cos x|=\log |c|$

or, $y\cos x=c$

or, $y=c\sec x$