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In Exercises 1 and 2, we consider the system dx 2x + 2y %3D dt dy = x + 3y. dt For the given function Y(t) = (a(t), y(t)), determine if Y(t) is a solution system. 1. (æ(t), y(t)) = (3e + e', -e' + e“) 2. 3. Consider the partially decoupled system dr Dorive the genorel solut

In Exercises 1 and 2, we consider the system dx 2x + 2y %3D dt dy = x + 3y. dt For the given function Y(t) = (a(t), y(t)), determine if Y(t) is a solution system. 1. (æ(t), y(t)) = (3e + e', -e' + e“) 2. 3. Consider the partially decoupled system dr Dorive the genorel solut

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 2.4 In Exercises 1 and 2, we consider the system da = 2x + 2y dt dy = x + 3y. dt For the given function Y(t) = (x (t), y(t)), determine if Y(t) is a solution system. 1. (a(t), y(t)) = (3e²" + e', –e' + e*) 2. (a(t), y(t)) = (4e' + e", –2e' + e^“) 3. Consider the partially decoupled system dx = 2x – 8y2 dt (a) Derive the general solution. (b) Find the equilibrium points of the system. dy = -3y. dt (c) Find the solution that satisfies the initial condition (xo, yo) = (0, 1).
Transcribed Image Text:Section 2.4 In Exercises 1 and 2, we consider the system da = 2x + 2y dt dy = x + 3y. dt For the given function Y(t) = (x (t), y(t)), determine if Y(t) is a solution system. 1. (a(t), y(t)) = (3e²" + e', –e' + e*) 2. (a(t), y(t)) = (4e' + e", –2e' + e^“) 3. Consider the partially decoupled system dx = 2x – 8y2 dt (a) Derive the general solution. (b) Find the equilibrium points of the system. dy = -3y. dt (c) Find the solution that satisfies the initial condition (xo, yo) = (0, 1).
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