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 n=e^(x)+c`

Answer

B

Explanation

Given, `(dy)/(dx)-ytan x=e^(x)secx`
`thereforelF=e^(-inttanxx dx)=e^(-logsec x)`
`=(1)/(sec x)`
`therefore` Complete solution is
`y*(1)/(sec x)=inte^(x)sec x*(1)/(sec x)dx`
`implies(y)/(sec x) =e^(x)+c`
`impliesy cos x=e^(x)+c`