Q. 37 O4.0( 2 Votes )

Solve each of the following initial value problems:

, tan x ≠ 0 given that y = 0 when

Answer :

, tan x ≠ 0 given that y = 0 when

Given and

This is a first order linear differential equation of the form

Here, P = cot x and Q = 2x + x2 cot 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,


y sin x = x2sin x + c

However, when, we have y = 0

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

Thus, the solution of the given initial value problem is

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