# Differential Equations and Green's Functions

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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).

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##### Solution Summary

Differential Equations and Green's Functions are investigated. The solution is detailed and well presented.

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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 ...

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