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In exercises 1-3, convert each of the following first order initial value problem to a Volterra integral equation: (1) y' + y = 0, y(0) = 1 (2) y'-y=x, y(0) = 0 (3) y' + y = sec²x, y(0) = 0

In exercises 1-3, convert each of the following first order initial value problem to a Volterra integral equation: (1) y' + y = 0, y(0) = 1 (2) y'-y=x, y(0) = 0 (3) y' + y = sec²x, y(0) = 0

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 59E: According to the solution in Exercise 58 of the differential equation for Newtons law of cooling,...
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Exercises 1.5 In exercises 1-3, convert each of the following first order initial value problem to a Volterra integral equation: (1) y' + y = 0, y(0) = 1 (2) y'-y = x, y(0) = 0 (3) y' + y = sec²x, y(0) = 0 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' + e*y = x, y(0) = 1, y'(0) = −1 In exercises 11-15, convert each of the following initial value problems of higher order to an equivalent Volterra integral equation: (11) y" − y" − y' + y = 0, y(0) = 2, y'(0) = 0, y" (0) = 2 (12) y"'+ 4y = x, y(0) = 0, y'(0) = 0, y" (0) = 1 (13) y +2y"+y = 3x + 4, y(0) = 0, y'(0) = 0, y"(0) = 1, y"'(0) = 1 (14) y - y = 0, y(0) = 1, y'(0) = 0, y" (0) = -1, y"'(0) = 0 (15) yiv+y"=2e, y(0) = 2, y'(0) = 2, y"(0) = 1, y"(0) = 1
Transcribed Image Text:Exercises 1.5 In exercises 1-3, convert each of the following first order initial value problem to a Volterra integral equation: (1) y' + y = 0, y(0) = 1 (2) y'-y = x, y(0) = 0 (3) y' + y = sec²x, y(0) = 0 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' + e*y = x, y(0) = 1, y'(0) = −1 In exercises 11-15, convert each of the following initial value problems of higher order to an equivalent Volterra integral equation: (11) y" − y" − y' + y = 0, y(0) = 2, y'(0) = 0, y" (0) = 2 (12) y"'+ 4y = x, y(0) = 0, y'(0) = 0, y" (0) = 1 (13) y +2y"+y = 3x + 4, y(0) = 0, y'(0) = 0, y"(0) = 1, y"'(0) = 1 (14) y - y = 0, y(0) = 1, y'(0) = 0, y" (0) = -1, y"'(0) = 0 (15) yiv+y"=2e, y(0) = 2, y'(0) = 2, y"(0) = 1, y"(0) = 1
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ISBN:
9780321964038
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