Find the general solution of the differential equation

Given

This is a first order linear differential equation of the form

Here, P = –1 and Q = cos x

The integrating factor (I.F) of this differential equation is,

We have

∴ I.F = e^–x

Hence, the solution of the differential equation is,

Let

⇒ I = e^–x(sin x – cos x) – I

⇒ 2I = e^–x(sin x – cos x)

By substituting the value of I in the original integral, we get

Thus, the solution of the given differential equation is