You are given the following simultaneous linear differential equations: dx/dt = x dy/dt = x - y 1. Express the system of equations in matrix form 2. Find the eigenvalues and eigenvectors of the matrix of coefficients 3. Hence or otherwise find the general solution of this system

You are given the following simultaneous linear differential equations: dx/dt = x dy/dt = x - y 1. Express the system of equations in matrix form 2. Find the eigenvalues and eigenvectors of the matrix of coefficients 3. Hence or otherwise find the general solution of this system

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

You are given the following simultaneous linear differential equations:

dx/dt = x

dy/dt = x - y

1. Express the system of equations in matrix form

2. Find the eigenvalues and eigenvectors of the matrix of coefficients

3. Hence or otherwise find the general solution of this system

With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.

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