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, and
The integrating factor (I.F) of this differential equation is,
We have
[∵ m log a = log am]
∴ I.F = x–1 [∵ elog x = x]
Hence, the solution of the differential equation is,
Let
By substituting this in the above integral, we get
We know
∴ y = –e–x + cx
Thus, the solution of the given differential equation is y = –e–x + cx