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1. Find the eigenvalues of the coefficient matrices of the following ODES. 2. Solve the Homogeneous systems (Show the steps) = 3y₁ - 4y2 y'2 = 3y2

1. Find the eigenvalues of the coefficient matrices of the following ODES. 2. Solve the Homogeneous systems (Show the steps) = 3y₁ - 4y2 y'2 = 3y2

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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Question 1 1. Find the eigenvalues of the coefficient matrices of the following ODES. 2. Solve the Homogeneous systems (Show the steps) (1) {'₁ = 33/₁-4/2 y'2 = 3y2 (2) {'₁=3y₁ - 4y/2 Y'2 = -2y2 (3) (4)(1-3y1-4y2 y2 = 3y₁ + 3y2 (y₁ = y₁ + 4y₂ ly/2 = -y₁ + 2y₂ Question 2 Consider the following first-order linear nonhomogeneous systems of ODES: 1. Solve the homogeneous systems (Show the steps) 2. Solve the nonhomogeneous systems (1) (3) y₁=-₁-6y₂ + 2 y2 = ₁ + 4y2-3 1=₁+ y2 + 10cos(t) (2) y'₂ = 3y1 - y2 - 10sin(t) y₁ (1) 1, y2 (1) = 0 y'₁ = y₂ +e³t y₂ = y₁-e³t (y₁ (1)= 1, y₂(1) = 0
Transcribed Image Text:Question 1 1. Find the eigenvalues of the coefficient matrices of the following ODES. 2. Solve the Homogeneous systems (Show the steps) (1) {'₁ = 33/₁-4/2 y'2 = 3y2 (2) {'₁=3y₁ - 4y/2 Y'2 = -2y2 (3) (4)(1-3y1-4y2 y2 = 3y₁ + 3y2 (y₁ = y₁ + 4y₂ ly/2 = -y₁ + 2y₂ Question 2 Consider the following first-order linear nonhomogeneous systems of ODES: 1. Solve the homogeneous systems (Show the steps) 2. Solve the nonhomogeneous systems (1) (3) y₁=-₁-6y₂ + 2 y2 = ₁ + 4y2-3 1=₁+ y2 + 10cos(t) (2) y'₂ = 3y1 - y2 - 10sin(t) y₁ (1) 1, y2 (1) = 0 y'₁ = y₂ +e³t y₂ = y₁-e³t (y₁ (1)= 1, y₂(1) = 0
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