Solve the following differential equation: `cos^2x(dy)/(dx)+y=tanx`

Explanation

Given, `cos ^{2} x frac{d y}{d x}+y=tan x`

`Rightarrow frac{{dy}}{{dx}}+{y} sec ^{2} {x}=tan {x} sec ^{2} {x}` ……… (1)

Here, `P=sec ^{2} x Rightarrow int P d P=int sec ^{2} x d x=tan x`

`therefore` I.F. `={e}^{tan x}`

Multiplying (1) by I.F ,

we get,

`e^{tan x} frac{d y}{d x}+e^{tan x} y sec ^{2} x=e^{tan x} tan x sec ^{2} x`

Integrating both sides,

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