Question

Find the solution of the differential equation:

$\tan xdy-\tan ydx=0$.

Answer 1

Given the differential equation:

$\tan xdy-\tan ydx=0$

or $\frac{dx}{\tan x}=\frac{dy}{\tan y}$

Now integrating both sides we have

$\log |secx|=\log |\sec y|+\log |c|$ [Where $c$ is integrating constant]

or, $|\sec x|=|c\sec y|$.