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Which of the following statements are true for this initial value problem? Select all that apply. dy (y - 4) = x - 6 with y (6) = 4 dx O y = x - 2 is the only solution of this initial-value problem. O y = x - 2 and y = 10 - x are both solutions of this initial value problem. This initial-value problem cannot have a solution because the conditions of the existence and uniqueness theorem for first-order linear equations are not satisfied. □ A locally unique solution is not guaranteed to exist by the local existence and uniqueness theorem for first-order x-6 differential equations because is not continuous at the point (6, 4). y-4 O The existence and uniqueness theorem for first-order linear equations ensures the existence of a unique local solution of this initial value problem because x - 6 is continuous at the point (6,4).

Which of the following statements are true for this initial value problem? Select all that apply. dy (y - 4) = x - 6 with y (6) = 4 dx O y = x - 2 is the only solution of this initial-value problem. O y = x - 2 and y = 10 - x are both solutions of this initial value problem. This initial-value problem cannot have a solution because the conditions of the existence and uniqueness theorem for first-order linear equations are not satisfied. □ A locally unique solution is not guaranteed to exist by the local existence and uniqueness theorem for first-order x-6 differential equations because is not continuous at the point (6, 4). y-4 O The existence and uniqueness theorem for first-order linear equations ensures the existence of a unique local solution of this initial value problem because x - 6 is continuous at the point (6,4).

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 17EQ
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Which of the following statements are true for this initial value problem? Select all that apply. dy (y-4) = x 6 with y (6) = 4 dx y = x 2 is the only solution of this initial-value problem. y = x - 2 and y = 10 x are both solutions of this initial value problem. O This initial-value problem cannot have a solution because the conditions of the existence and uniqueness theorem for first-order linear equations are not satisfied. A locally unique solution is not guaranteed to exist by the local existence and uniqueness theorem for first-order x-6 is not continuous at the point (6, 4). y - 4 differential equations because O The existence and uniqueness theorem for first-order linear equations ensures the existence of a unique local solution of this initial value problem because x - 6 is continuous at the point (6, 4).
Transcribed Image Text:Which of the following statements are true for this initial value problem? Select all that apply. dy (y-4) = x 6 with y (6) = 4 dx y = x 2 is the only solution of this initial-value problem. y = x - 2 and y = 10 x are both solutions of this initial value problem. O This initial-value problem cannot have a solution because the conditions of the existence and uniqueness theorem for first-order linear equations are not satisfied. A locally unique solution is not guaranteed to exist by the local existence and uniqueness theorem for first-order x-6 is not continuous at the point (6, 4). y - 4 differential equations because O The existence and uniqueness theorem for first-order linear equations ensures the existence of a unique local solution of this initial value problem because x - 6 is continuous at the point (6, 4).
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