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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. 2. (x(t), y(t)) = (4e' + e" -2e' + e")

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. 2. (x(t), y(t)) = (4e' + e" -2e' + e")

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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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. 2. (æ(t), y(t)) = (4e' + e“, –2e' + e“") 3. Consider the partially decoupled system dx 8y? (a) Derive the general solution. = 2x - dt (b) Find the equilibrium points of the system. dy = -3y. dt (c) Find the solution that satisfies the initial condition (co, 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. 2. (æ(t), y(t)) = (4e' + e“, –2e' + e“") 3. Consider the partially decoupled system dx 8y? (a) Derive the general solution. = 2x - dt (b) Find the equilibrium points of the system. dy = -3y. dt (c) Find the solution that satisfies the initial condition (co, yo) = (0, 1).
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