Math Help Differential Equation

Find all solutions of the equation

y’ + 2y = b(x) , (−∞ < x < +∞)

where

1 − |x|, se |x| ≤ 1

b(x) = 0, se |x| > 1

Solution

It is unclear what “se” means, but b(x) is simply a function defined on 2 intervals, then

the d.e. needs to be solved in 3 interval, x<0, 0<x<1, and x>1.

In the left interval and the middle interval e2x is an integrating factor and in the right interval the equation is homogenous…and in each interval the solution is quite easy.