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The general solution of (dy)/(dx)+y tan ...

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

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`

Text Solution

Verified by Experts

The correct Answer is:
A
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`
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