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Section 1.5 In Exercises 1 and 2, we refer to a function f, but we do not provide its formula. However, we do assume that f satisfies th hypothesis of the Uniqueness Theorem in the entire ty-plane, and we do provide various solutions to the given differentia equation. Finally, we specify an initial condition. Using the Uniqueness Theorem, what can you conclude about th solution to the equation with the given initial condition? dy dy 1. = f(t, y) dt 2. f(t, y) %3D y1(t) = 4 for all t is a solution, y2(t) = 2 for all t is a solution, y3(t) = 0 for all t is a solution, initial condition y(0) = 1. dt yı(t) = -1 for all t is a solution, Y2 (t) = 1+ t² for all t is a solution, initial condition y(0) = 0.

Section 1.5 In Exercises 1 and 2, we refer to a function f, but we do not provide its formula. However, we do assume that f satisfies th hypothesis of the Uniqueness Theorem in the entire ty-plane, and we do provide various solutions to the given differentia equation. Finally, we specify an initial condition. Using the Uniqueness Theorem, what can you conclude about th solution to the equation with the given initial condition? dy dy 1. = f(t, y) dt 2. f(t, y) %3D y1(t) = 4 for all t is a solution, y2(t) = 2 for all t is a solution, y3(t) = 0 for all t is a solution, initial condition y(0) = 1. dt yı(t) = -1 for all t is a solution, Y2 (t) = 1+ t² for all t is a solution, initial condition y(0) = 0.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 70EQ
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Section 1.5 In Exercises 1 and 2, we refer to a function ƒ, but we do not provide its formula. However, we do assume that f satisfies th hypothesis of the Uniqueness Theorem in the entire ty-plane, and we do provide various solutions to the given differentia equation. Finally, we specify an initial condition. Using the Uniqueness Theorem, what can you conclude about th solution to the equation with the given initial condition? dy 1. = f(t, y) dt dy 2. = f(t, y) dt yı(t) = 4 for all t is a solution, Y2(t) = 2 for all t is a solution, Y3(t) = 0 for all t is a solution, initial condition y(0) = 1. y1 (t) = -1 for all t is a solution, y2 (t) = 1+ t2 for all t is a solution, initial condition y(0) = 0.
Transcribed Image Text:Section 1.5 In Exercises 1 and 2, we refer to a function ƒ, but we do not provide its formula. However, we do assume that f satisfies th hypothesis of the Uniqueness Theorem in the entire ty-plane, and we do provide various solutions to the given differentia equation. Finally, we specify an initial condition. Using the Uniqueness Theorem, what can you conclude about th solution to the equation with the given initial condition? dy 1. = f(t, y) dt dy 2. = f(t, y) dt yı(t) = 4 for all t is a solution, Y2(t) = 2 for all t is a solution, Y3(t) = 0 for all t is a solution, initial condition y(0) = 1. y1 (t) = -1 for all t is a solution, y2 (t) = 1+ t2 for all t is a solution, initial condition y(0) = 0.
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