Q. 37 K5.0( 1 Vote )

Solve each of the following initial value problems:

, y = 0 when

Answer :

xi. , y = 0 when

Given and

This is a first order linear differential equation of the form

Here, P = 2 tan x and Q = sin x

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

We have

[ m log a = log am]

I.F = sec2x [ elog x = x]

Hence, the solution of the differential equation is,


ysec2x = sec x + c

y = cos x + c cos2x

However, when, we have y = 0

c = –2

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

y = cos x + (–2)cos2x

y = cos x – 2cos2x

Thus, the solution of the given initial value problem is y = cos x – 2cos2x

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