Q. 37 A5.0( 1 Vote )

Solve each of the following initial value problems:

y’ + y = ex,

Answer :

y’ + y = ex,

Given y’ + y = ex and

This is a first order linear differential equation of the form

Here, P = 1 and Q = ex

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

We have

I.F = ex

Hence, the solution of the differential equation is,


However, when x = 0, we have

c = 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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