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(a) Find the largest interval on which Theorem 3.1.1 guarantees that the following initial value problem has a unique solution. (x + 2) y'' + (x² − 64) y″ + 14y y(0) = 0, y'(0) = 8, y'(0) = 8 x-4 (b) Find the largest interval on which Theorem 3.1.1 guarantees that the following initial value problem has a unique solution. (x − 2) y'" + (x² − 64) y" + 14y x-4 3 2 y(0) = 0, y'(0) = 8, y"(0) = 8

(a) Find the largest interval on which Theorem 3.1.1 guarantees that the following initial value problem has a unique solution. (x + 2) y'' + (x² − 64) y″ + 14y y(0) = 0, y'(0) = 8, y'(0) = 8 x-4 (b) Find the largest interval on which Theorem 3.1.1 guarantees that the following initial value problem has a unique solution. (x − 2) y'" + (x² − 64) y" + 14y x-4 3 2 y(0) = 0, y'(0) = 8, y"(0) = 8

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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Theorem 3.1.1 Existence of a Unique Solution Let añ(x), an−1(x), . . .‚ α₁(x), a(x), and g(x) be continuous on an interval I, and let a„(x) ‡ 0 for every x in this interval. If x xo is any point in this interval, then a solution y(x) of the initial-value problem (1) exists on the interval and is unique. =
Transcribed Image Text:Theorem 3.1.1 Existence of a Unique Solution Let añ(x), an−1(x), . . .‚ α₁(x), a(x), and g(x) be continuous on an interval I, and let a„(x) ‡ 0 for every x in this interval. If x xo is any point in this interval, then a solution y(x) of the initial-value problem (1) exists on the interval and is unique. =
(a) Find the largest interval on which Theorem 3.1.1 guarantees that the following initial value problem has a unique solution. (x+2) y'"' + (x² − 64) y″ + 14y = - = 4, y(0) = 0, y'(0) = 8, y″(0) = 8 X- (b) Find the largest interval on which Theorem 3.1.1 guarantees that the following initial value problem has a unique solution. 1 (x − 2) y'"' + (x² − 64) y″ + 14y = -¹4; _y(0)= 0, y'(0) = 8, y″(0) = 8 X- |(A) (−4,−2) (B) (−2, ∞) (C) (2, ∞) (D) (-∞, -4) (E) (-∞, 4) (F) (-4,2) (G) (2,4) (H) (4, ∞) (I) (−4, ∞0) |(J) (−2, 4) (K) (-∞, 2) (L) (-∞, -2) |(A) (−4, 2) (B) (2,4) (C) (-∞,−4) (D) (2, ∞) (E) (-4, ∞) (F) (-4,-2) (G) (-∞, 4) (H) (-∞, −2) (I) (4, ∞) |(J) (−2, ∞) (K) (-∞, 2) (L) (−2, 4)
Transcribed Image Text:(a) Find the largest interval on which Theorem 3.1.1 guarantees that the following initial value problem has a unique solution. (x+2) y'"' + (x² − 64) y″ + 14y = - = 4, y(0) = 0, y'(0) = 8, y″(0) = 8 X- (b) Find the largest interval on which Theorem 3.1.1 guarantees that the following initial value problem has a unique solution. 1 (x − 2) y'"' + (x² − 64) y″ + 14y = -¹4; _y(0)= 0, y'(0) = 8, y″(0) = 8 X- |(A) (−4,−2) (B) (−2, ∞) (C) (2, ∞) (D) (-∞, -4) (E) (-∞, 4) (F) (-4,2) (G) (2,4) (H) (4, ∞) (I) (−4, ∞0) |(J) (−2, 4) (K) (-∞, 2) (L) (-∞, -2) |(A) (−4, 2) (B) (2,4) (C) (-∞,−4) (D) (2, ∞) (E) (-4, ∞) (F) (-4,-2) (G) (-∞, 4) (H) (-∞, −2) (I) (4, ∞) |(J) (−2, ∞) (K) (-∞, 2) (L) (−2, 4)
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