Solve the following differential equations:
Given
[∵ x2 – 1 = (x + 1)(x – 1)]
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 and
[∵ m log a = log am]
[∵ log a + log b = log ab]
[∵ elog x = x]
Hence, the solution of the differential equation is,
We can write (x – 1)2 = (x + 1)2 – 4x
Recall and
Thus, the solution of the given differential equation is