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a. Find the eigenvalues and corresponding eigenvectors for the matrix P = A₁ = -2 x₁(t)= x₂ (1) = c1e^t+c2e^-t c1e^t(1.3333)+c2e^-t 7₁ = 1.33333 1 -17 20 -15 18 , and ₂3 1 b. Find the most general solution to the linear system of differential equations x' = Px. Use c₁ and c₂ to denote arbitrary constants, and enter them as c1 and c2. 1

a. Find the eigenvalues and corresponding eigenvectors for the matrix P = A₁ = -2 x₁(t)= x₂ (1) = c1e^t+c2e^-t c1e^t(1.3333)+c2e^-t 7₁ = 1.33333 1 -17 20 -15 18 , and ₂3 1 b. Find the most general solution to the linear system of differential equations x' = Px. Use c₁ and c₂ to denote arbitrary constants, and enter them as c1 and c2. 1

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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a. Find the eigenvalues and corresponding eigenvectors for the matrix P = A₁ = -2 x₁1(t)= cle^t(1.3333)+c2e^-t 7₁ x₂(t)=c1e^t+c2e^-t = 1.33333 1 b. Find the most general solution to the linear system of differential equations as c1 and c2. -17 20 -15 18 and ₂ = 3 1 1 = Px. Use c₁ and c₂ to denote arbitrary constants, and enter them
Transcribed Image Text:a. Find the eigenvalues and corresponding eigenvectors for the matrix P = A₁ = -2 x₁1(t)= cle^t(1.3333)+c2e^-t 7₁ x₂(t)=c1e^t+c2e^-t = 1.33333 1 b. Find the most general solution to the linear system of differential equations as c1 and c2. -17 20 -15 18 and ₂ = 3 1 1 = Px. Use c₁ and c₂ to denote arbitrary constants, and enter them
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