Consider the following system of second-order differential equations: x ̈ = −0.7x + 0.9y, y ̈ = 0.9x + 1.7y. The coefficient matrix is [-0.7 0.9] [0.9 1.7] and it has eigenvectors [1] [3] and [3] [-1] Calculate the eigenvalues that correspond to the given eigenvectors and then write down the general solution of the given system of second-order differential equations

Consider the following system of second-order differential equations: x ̈ = −0.7x + 0.9y, y ̈ = 0.9x + 1.7y. The coefficient matrix is [-0.7 0.9] [0.9 1.7] and it has eigenvectors [1] [3] and [3] [-1] Calculate the eigenvalues that correspond to the given eigenvectors and then write down the general solution of the given system of second-order differential equations

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

Consider the following system of second-order differential equations:

x ̈ = −0.7x + 0.9y,
y ̈ = 0.9x + 1.7y.

The coefficient matrix is

[-0.7 0.9]
[0.9 1.7]

and it has eigenvectors

[1]
[3]

and

[3]
[-1]

Calculate the eigenvalues that correspond to the given eigenvectors and then write down the general solution of the given system of second-order differential equations.

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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