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 Q = x2 + 2
The integrating factor (I.F) of this differential equation is,
We have
[∵ m log a = log am]
[∵ elog x = x]
Hence, the solution of the differential equation is,
Recall and
∴ y = (x2 + 1)(x + tan–1x + c)
Thus, the solution of the given differential equation is y = (x2 + 1)(x + tan–1x + c)