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Theorem 1- Existence of a Unique Solution Consider the initial value problem (IVP) = f (x, y) , y (xo) = Yo- Let R be a rectangular region in %3D Ty plane defined by a <¤ < b,c < y < d that contains the point (#o, Yo) in its interior. If f (x, y) af are continuous on R, then there exists some interval In : #0 – h < æ < ¤o+h, h > 0 and contained in a < x < b, and a unique function y (x), define on I, that is a solution of the given IVP. Given f (x, y) = (y² – 9) i. Examine which of the given points possesses a unique solution according to the Theorem 1? a. (1,4) b. (5,3) c. (2,-3) O d. (-1,1)

Theorem 1- Existence of a Unique Solution Consider the initial value problem (IVP) = f (x, y) , y (xo) = Yo- Let R be a rectangular region in %3D Ty plane defined by a <¤ < b,c < y < d that contains the point (#o, Yo) in its interior. If f (x, y) af are continuous on R, then there exists some interval In : #0 – h < æ < ¤o+h, h > 0 and contained in a < x < b, and a unique function y (x), define on I, that is a solution of the given IVP. Given f (x, y) = (y² – 9) i. Examine which of the given points possesses a unique solution according to the Theorem 1? a. (1,4) b. (5,3) c. (2,-3) O d. (-1,1)

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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Theorem 1- Existence of a Unique Solution Consider the initial value problem (IVP) 2 = f (x, y) , y (xo) = Yo- Let R be a rectangular region in Ty plane defined by a < ¤ < b,c < y < d that contains the point (#o, Yo) in its interior. If f (x, y) af are continuous on R, then there exists some interval Io : ¤o – h <x < To + h, h > 0 and contained in a < I < b, and a unique function y (x), define on Ig, that is a solution of the given IVP. Given f (x, y) = (y² – 9) 3. Examine which of the given points possesses a unique solution according to the Theorem 1? а. (1,4) b. (5,3) с. (2.-3) Od. (-1,1)
Transcribed Image Text:Theorem 1- Existence of a Unique Solution Consider the initial value problem (IVP) 2 = f (x, y) , y (xo) = Yo- Let R be a rectangular region in Ty plane defined by a < ¤ < b,c < y < d that contains the point (#o, Yo) in its interior. If f (x, y) af are continuous on R, then there exists some interval Io : ¤o – h <x < To + h, h > 0 and contained in a < I < b, and a unique function y (x), define on Ig, that is a solution of the given IVP. Given f (x, y) = (y² – 9) 3. Examine which of the given points possesses a unique solution according to the Theorem 1? а. (1,4) b. (5,3) с. (2.-3) Od. (-1,1)
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