You have been given the following points below. For which of the points does theorem 1.2.1 guarantee that the differential equation=√₁2-36 possesses a unique solution through the given point? There can be more than one right answer. a) (3,8) b) (1,6) c) (-3,5) THEOREM 1.2.1 (Existence of a Unique Solution) Let R be a rectangular region in the xy-plane defined by a ≤ x ≤ b, c ≤ y ≤d that contains the point (x, yo) in its interior. If f(x, y) and af/ay are continuous on R, then there exists some interval lo: (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).
You have been given the following points below. For which of the points does theorem 1.2.1 guarantee that the differential equation=√₁2-36 possesses a unique solution through the given point? There can be more than one right answer. a) (3,8) b) (1,6) c) (-3,5) THEOREM 1.2.1 (Existence of a Unique Solution) Let R be a rectangular region in the xy-plane defined by a ≤ x ≤ b, c ≤ y ≤d that contains the point (x, yo) in its interior. If f(x, y) and af/ay are continuous on R, then there exists some interval lo: (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).
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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Question
![You have been given the following points below. For which of
the points does theorem 1.2.1 guarantee that the differential
equation=√₁2-36
possesses a unique solution through the
given point? There can be more than one right answer.
a) (3,8)
b) (1,6)
c) (-3,5)
THEOREM 1.2.1 (Existence of a Unique Solution)
Let R be a rectangular region in the xy-plane defined by a ≤ x ≤ b, c ≤ y ≤ d that contains the
point (xo, Yo) in its interior. If f(x, y) and af/ay are continuous on R, then there exists some interval
lo: (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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F59dcb7e3-ba5c-4029-b6e3-e5c03331d9db%2F4b06ed8e-2936-434e-8fe8-b687a9db100b%2Fi1yeqps_processed.jpeg&w=3840&q=75)
Transcribed Image Text:You have been given the following points below. For which of
the points does theorem 1.2.1 guarantee that the differential
equation=√₁2-36
possesses a unique solution through the
given point? There can be more than one right answer.
a) (3,8)
b) (1,6)
c) (-3,5)
THEOREM 1.2.1 (Existence of a Unique Solution)
Let R be a rectangular region in the xy-plane defined by a ≤ x ≤ b, c ≤ y ≤ d that contains the
point (xo, Yo) in its interior. If f(x, y) and af/ay are continuous on R, then there exists some interval
lo: (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).
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