Q. 36 G5.0( 1 Vote )

# Find one-parameter families of solution curves of the following differential equations:

Answer :

Given

This is a first order linear differential equation of the form

Here, P = cos x and Q = esin x cos x

The integrating factor (I.F) of this differential equation is,

We have

I.F = esin x

Hence, the solution of the differential equation is,

Let sin x = t

cosxdx = dt [Differentiating both sides]

By substituting this in the above integral, we get

Recall

[ t = sin x]

Thus, the solution of the given differential equation is

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