Assignment:
Consider the inhomogeneous differential equation
-u’ + u = r(x) on (a,b)
where r(x) is a continuous function on the interval (a,b). Find the solution to this differential equation in the form u = integral from a to b (G(x,s) r(s) ds) and determine G(x,s).
Provide complete and step by step solution for the question and show calculations and use formulas.