The solution of the differential equation `(dy)/(dx)-y tan x=e^(x)sec x` is

Options

A. `y= e^(x) cos x +C`
B. `y cos x =e^(x) +C`
C. ` y = e^(x) sin x +C`
D. `y sin x = e^(x) +C`

Answer

b

Explanation

Given , ` (dy)/(dx) - y tan x = e^(x) sec x `
` :. IF = e^(- int tan x dx ) = e^(-logsec x)=1/(secx)`
` :. ` General solution is
` rArr y * 1/(sec x) = int e^(x) sec x * 1/(sec x) dx`
` rArr y cos x = e^(x) + C`