Q. 36 E5.0( 1 Vote )

# 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

[ t = log x]

Thus, the solution of the given differential equation is

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