Question

Verify that the given function is a solution of the differential equation. y sec x = tan x + c; $\frac{dy}{dx}+y\tan x = \sec x$

Answer 1

To verify that the given function is a solution of the differential equation. y sec x = tan x + c;

$\frac{dy}{dx}+y\tan x = \sec x$

calculate dy/dx from given equation,and convert

$y \: sec \: x = tan \: x + c \\ \\ y \: sec \: x \: tan \: x + sec \: x \frac{dy}{dx} = {sec}^{2} \: x$

taking sec x common

$sec \: x \: (y \: tan \: x + \frac{dy}{dx}) = {sec}^{2} \: x \\ \\ (y \: tan \: x + \frac{dy}{dx}) = sec \: x$
is the desired equation.