Find one-parameter families of solution curves of the following differential equations:
Given
This is a first order linear differential equation of the form
Here, P = –1 and Q = cos 2x
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
⇒ 5I = e–x(2 sin 2x – cos 2x)
By substituting the value of I in the original integral, we get
Thus, the solution of the given differential equation is