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sider the system of differential equations x= 10/3x1 + 4/3x2 x2 = 8/3x1 +14/3x2' ere 1 and 2 are functions of t. Our goal is first to find the general solution of this system and then a particular solution. v AV

sider the system of differential equations x= 10/3x1 + 4/3x2 x2 = 8/3x1 +14/3x2' ere 1 and 2 are functions of t. Our goal is first to find the general solution of this system and then a particular solution. v AV

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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Consider the system of differential equations ab sin (a) where 1 and 2 are functions of t. Our goal is first to find the general solution of this system and then a particular solution. a) This system can be written using matrices as X' = AX, where X is in R2 and the matrix A is A = əx = and X₂= 8 Eigenvalues: Give an eigenvector associated to the smallest eigenvalue. Give an eigenvector associated to the largest eigenvalue. Answer: a Ω b) Find the eigenvalues and eigenvectors of the matrix A associated to the system of linear differential equatons. List the eigenvalues separated semicolons. x₁ = 10/3x1 + 4/3x2 x=8/3x1 +14/3x2 c) The general solution of the system of linear differential equations is of the form X = c₁ X₁ + c2X2, where c₁ and co are constants, and X1 Answer: X(t) = - (21 (6)) = d) Find the solution if the initial condition is - B " We assume that X₁ is assoicated to the smallest eigenvalue and X2 to the largest eigenvalue. Use the scientific calculator notation. For instance 3e written 3*e^(-4*t). -3 (21) - (2³) at t = at t = 0. -4t is
Transcribed Image Text:Consider the system of differential equations ab sin (a) where 1 and 2 are functions of t. Our goal is first to find the general solution of this system and then a particular solution. a) This system can be written using matrices as X' = AX, where X is in R2 and the matrix A is A = əx = and X₂= 8 Eigenvalues: Give an eigenvector associated to the smallest eigenvalue. Give an eigenvector associated to the largest eigenvalue. Answer: a Ω b) Find the eigenvalues and eigenvectors of the matrix A associated to the system of linear differential equatons. List the eigenvalues separated semicolons. x₁ = 10/3x1 + 4/3x2 x=8/3x1 +14/3x2 c) The general solution of the system of linear differential equations is of the form X = c₁ X₁ + c2X2, where c₁ and co are constants, and X1 Answer: X(t) = - (21 (6)) = d) Find the solution if the initial condition is - B " We assume that X₁ is assoicated to the smallest eigenvalue and X2 to the largest eigenvalue. Use the scientific calculator notation. For instance 3e written 3*e^(-4*t). -3 (21) - (2³) at t = at t = 0. -4t is
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