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For what value yo does the initial value problem y = Vy² – 9 with y(xo) = yo have a unique solution guaranteed by the theorem above?

For what value yo does the initial value problem y = Vy² – 9 with y(xo) = yo have a unique solution guaranteed by the theorem above?

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 1.2.1 Existence of a Unique Solution Let R be a rectangular region in the æy-plane defined by a < x < b, c <y< d that contains the point (xo, Yo) in its interior. If f(x, y) and f/dy are continuous on R, then there exists some interval Io: (xo – h, xo + h), h > 0, contained in [a, b), and a unique function y(x), defined on I,, that is a solution of the initial-value problem (2). For what value yo does the initial value problem y = Vy² – 9 with y(xo) = yo have a unique solution guaranteed by the theorem above? Select the correct answer. O yo = 3 O yo = -3 Yo = 5 yo = 0 O yo = 1
Transcribed Image Text:Theorem 1.2.1 Existence of a Unique Solution Let R be a rectangular region in the æy-plane defined by a < x < b, c <y< d that contains the point (xo, Yo) in its interior. If f(x, y) and f/dy are continuous on R, then there exists some interval Io: (xo – h, xo + h), h > 0, contained in [a, b), and a unique function y(x), defined on I,, that is a solution of the initial-value problem (2). For what value yo does the initial value problem y = Vy² – 9 with y(xo) = yo have a unique solution guaranteed by the theorem above? Select the correct answer. O yo = 3 O yo = -3 Yo = 5 yo = 0 O yo = 1
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