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

Explanation

`cos^2x dy/dx+y = tanx`

`=>dy/dx + sec^2xy = tanxsec^2x`


Comparing the given equation with first order differential equation,

`dy/dx+Py = Q(x)`, we get,
`P = sec^2x and Q(x) = tanxsec^2x`

So, Integrating factor `(I.F) = e^(int sec^2xdx)`

`I.F.= e^(tanx)`

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