Q3. (a) If Ax = 2 x, determine the eigenvalues and the corresponding eigenvectors for A = Hence, write down the associated modal matrix P and diagonal matrix D, and use these values to solve the following system differential equations: * = X, +4 X2 *2 = 2 x1 + 3 x2 Given that when t= 0, x1 = 0 and x2 = 2. %3D %3D

Q3. (a) If Ax = 2 x, determine the eigenvalues and the corresponding eigenvectors for A = Hence, write down the associated modal matrix P and diagonal matrix D, and use these values to solve the following system differential equations: * = X, +4 X2 *2 = 2 x1 + 3 x2 Given that when t= 0, x1 = 0 and x2 = 2. %3D %3D

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

Can I have a clear written down step-by-step explanation, please?

The last expert typed the numbers up and it was confusing to follow and some numbers and equations got mixed up in that format.

Thank you

Q3.
(a) If Ax = 2 x, determine the eigenvalues and the corresponding eigenvectors for
A= G )
2 3.
Hence, write down the associated modal matrix P and diagonal matrix D, and
use these values to solve the following system differential equations:
*1 = X1 + 4 x2
X2 = 2 x1 + 3 x2
Given that when t = 0, x1 = 0 and x2 = 2.
(b) Use the 4th order Runge Kutta method to solve the differential equation:
dy
e* y
dx
for values of x 0 (0.2) 0.4 given that y 1 when x 0.
%3D
Give your answers correct to 5 decimal places.
Obtain the analytical solution of the differential equation and compare the
analytical solution when x = 0.4 with the values obtained using Runge Kutta,

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