Question

Write the integrating factor (I.F.) of the differential equation `(dy)/(dx) + y = e^-x`.

Answer 1

Given: `(dy)/(dx) + y + e^-x`

This is a linear differential equation of the form:

`(dy)/(dx) + P(x)y = Q(x)`

Here, P(x) = 1

Integrating Factor (I.F.) formula: 

I.F. = `e^(intP(x)dx) = e^(int1dx) = e^x`