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,
Let t = log x
[Differentiating both sides]
By substituting this in the above integral, we get
We have
⇒ I.F = elog t
⇒ I.F = t [∵ elog x = x]
∴ I.F = log x [∵ t = log x]
Hence, the solution of the differential equation is,
Let t = log x
[Differentiating both sides]
By substituting this in the above integral, we get
We know
⇒ yt = t2 + c
[∵ t = log x]
Thus, the solution of the given differential equation is