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In exercises 4-10, derive an equivalent Volterra integral equation to each of the following initial value problems of second order: (4) y"+y = 0, y(0) = 1, y'(0) = 0 (5) y"-y=0, y(0) = 1, y'(0) = 1 (6) y" +5 y' + 6y = 0, y(0) = 1, y'(0) = 1

In exercises 4-10, derive an equivalent Volterra integral equation to each of the following initial value problems of second order: (4) y"+y = 0, y(0) = 1, y'(0) = 0 (5) y"-y=0, y(0) = 1, y'(0) = 1 (6) y" +5 y' + 6y = 0, y(0) = 1, y'(0) = 1

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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In exercises 4-10, derive an equivalent Volterra integral equation to each of the following initial value problems of second order: (4) y"+y = 0, y(0) = 1, y'(0) = 0 (5) y" -y = 0, y(0) = 1, y'(0) = 1 (6) y" +5 y' + 6y = 0, y(0) = 1, y'(0) = 1 (7) y" + y'= 0, y(1) = 0, y'(1) = 1 (8) y"+y'- 2y = 2x, y(0) = 0, y'(0) = 1 (9) y"+y=sin x, y(0) = 0, y'(0) = 0 (10) y" - sinx y' + ey = x, y(0) = 1, y'(0) = -1
Transcribed Image Text:In exercises 4-10, derive an equivalent Volterra integral equation to each of the following initial value problems of second order: (4) y"+y = 0, y(0) = 1, y'(0) = 0 (5) y" -y = 0, y(0) = 1, y'(0) = 1 (6) y" +5 y' + 6y = 0, y(0) = 1, y'(0) = 1 (7) y" + y'= 0, y(1) = 0, y'(1) = 1 (8) y"+y'- 2y = 2x, y(0) = 0, y'(0) = 1 (9) y"+y=sin x, y(0) = 0, y'(0) = 0 (10) y" - sinx y' + ey = x, y(0) = 1, y'(0) = -1
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