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

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

Advanced Engineering Mathematics
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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Can we do this without the Leibniz Rule?

Let 9 be continuous on [a, b), and let f(x) = S (x – t)9(t) dt. Prove that f is a solution of the differential equation f" = g and the initial conditions f(a) = f'(a) = 0.
Transcribed Image Text:Let 9 be continuous on [a, b), and let f(x) = S (x – t)9(t) dt. Prove that f is a solution of the differential equation f" = g and the initial conditions f(a) = f'(a) = 0.
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