Q. 284.0( 2 Votes )

# Solve the following differential equations:

Answer :

Given

This is a first order linear differential equation of the form

Here, P = cos x and Q = sin 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

yet = tet – et + c

yet × e–t = (tet – et + c)e–t

y = t – 1 + ce–t

y = sin x – 1 + ce–sin x [ t = sin x]

Thus, the solution of the given differential equation is y = sin x – 1 + ce–sin x

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