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