Can we prove that the function (x-t)g(t) is continous given what we know from the problem definition? = S (x - t)g(t) dt.Let g be continuous on [a, b], and let f(x)Prove that f is a solution of the differential equation f" = g andthe initial conditions f(a) = f' (a) = 0.

Given that g be continuous on a, b and let f(x)=∫ax(x-a)g(t)dt. And we have to show that f is a…

Answered: Let g be continuous on [a, b), and let…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let g be continuous on [a, b), and let f(x) = S (x – t)g(t) dt. Prove that f is a solution of the differential equation f" = g and the initial conditions f(a) = f'(a) = 0.