Solve: `dy / dx + y secx = tanx`

Explanation

The given differential equation is


`frac{d y}{d x}+(sec {x}) {y}=tan {x}`


This is a linear differential equation of the form `frac{d y}{d x}+P y=Q`, where `P=sec x` and `Q` `=tan x`


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`therefore I F=e^{int P d x}=e^{int sec x d x}=e^{log (sec x+tan x)}=tan x(sec x+tan x)`


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Multiplying both sides of (i) by `{IF}=(sec x+tan x)`, we get


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