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5. Use the Fundamental Theorem of Calculus to show that the function u = u(t) is a solution to the initial value problem a' = f(t, æ) æ(to) = x0, if and only if u is a solution to the integral equation x(t) = xo+ | f(s, x(8)) ds.

5. Use the Fundamental Theorem of Calculus to show that the function u = u(t) is a solution to the initial value problem a' = f(t, æ) æ(to) = x0, if and only if u is a solution to the integral equation x(t) = xo+ | f(s, x(8)) ds.

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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I can get from the differential equation to the integral equation using the FTOC, but I'm not sure how to incorporate u=u(t) for the actual problem

5. Use the Fundamental Theorem of Calculus to show that the function u = u(t) is a solution to the initial value problem a' = f(t, x) x(to) = xo, if and only if u is a solution to the integral equation x(t) = xo + | f(s, 2(s)) ds.
Transcribed Image Text:5. Use the Fundamental Theorem of Calculus to show that the function u = u(t) is a solution to the initial value problem a' = f(t, x) x(to) = xo, if and only if u is a solution to the integral equation x(t) = xo + | f(s, 2(s)) ds.
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