Q. 37 M5.0( 1 Vote )

Solve each of the following initial value problems:


Answer :


Given and

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


yt = t2 + c

[ t = sin x]

However, when, we have y = 0

0 = 1 + c

c = –1

By substituting the value of c in the equation for y, we get

[ sin2θ + cos2θ = 1]

y = –cos x cot x

Thus, the solution of the given initial value problem is y = –cosec x cot x

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