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Consider the first order ODE y' = √y² – 9. Use the fundamental existence-uniqueness theorem (on page 2 of this document) to determine if the ODE is guaranteed to have a unique solution through the following points. a. (1,4) b. (2,-3)

Consider the first order ODE y' = √y² – 9. Use the fundamental existence-uniqueness theorem (on page 2 of this document) to determine if the ODE is guaranteed to have a unique solution through the following points. a. (1,4) b. (2,-3)

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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Consider the first order ODE y' = √√y²-9. Use the fundamental existence-uniqueness theorem (on page 2 of this document) to determine if the ODE is guaranteed to have a unique solution through the following points. a. (1,4) b. (2,-3) The Fundamental Existence-Uniqueness Theorem for a first order IVP y' = F(x, y), y(x) = yo If F (x, y) and OF(x,y) are real and continuous functions in a rectangle ду R = {(x, y): a < x < b, c <y<d} which contains the point (xo, Yo), then the IVP has a unique solution y = f(x) in some subinterval (xoh, xo + h) of (a, b).
Transcribed Image Text:Consider the first order ODE y' = √√y²-9. Use the fundamental existence-uniqueness theorem (on page 2 of this document) to determine if the ODE is guaranteed to have a unique solution through the following points. a. (1,4) b. (2,-3) The Fundamental Existence-Uniqueness Theorem for a first order IVP y' = F(x, y), y(x) = yo If F (x, y) and OF(x,y) are real and continuous functions in a rectangle ду R = {(x, y): a < x < b, c <y<d} which contains the point (xo, Yo), then the IVP has a unique solution y = f(x) in some subinterval (xoh, xo + h) of (a, b).
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