Q. 37 N5.0( 1 Vote )

# Solve each of the following initial value problems:dy = cos x (2 – y cosec x)dx

dy = cos x (2 – y cosec x)dx

Given dy = cos x (2 – y cosec x)dx

This is a first order linear differential equation of the form

Here, P = cot x and Q = 2 cos x

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

We have

I.F = sin x [ elog x = 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

yt = t2 + c

[ t = sin x]

Thus, the solution of the given differential equation is

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