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 a^m]

[∵ e^{log 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)