The general solution of `(dy)/(dx)+y tan x=sec x` is

Options

A. `y sec x=tanx+C`
B. `y tan x=sec x+C`
C. `tan x=y tan x+C`
D. `x sec x=tan y+C`

Answer

A

Explanation

Given differential equation is `(dy)/(dx)+y tan x=sec x`
Which is a linear differential equation ``P=tanx, Q=sec x`
`IF= e^(inttan xdx)=e^(log|sec x|)=secx`
The general solution is
`y.sec x =intsecx.secx+C`
`Rightarrow y.sec x =intsec^(2)xdx+C`
`Rightarrow y.sec x =tanx+C`