Q3. (a) If Ax = 2 x, determine the eigenvalues and the corresponding eigenvectors for A = Henoe, write down the associated modal matrix P and diagonal matrix D, and use these values to solve the following system differential equations: * = X1 + 4 x2 *2 = 2 x1 + 3 X2 Given that whent = 0, x, = 0 and x2 = 2.
Q3. (a) If Ax = 2 x, determine the eigenvalues and the corresponding eigenvectors for A = Henoe, write down the associated modal matrix P and diagonal matrix D, and use these values to solve the following system differential equations: * = X1 + 4 x2 *2 = 2 x1 + 3 X2 Given that whent = 0, x, = 0 and x2 = 2.
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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Transcribed Image Text:Q3.
(a)
If Ax = 2 x, determine the eigenvalues and the corresponding eigenvectors for
(1
A
2
Hence, write down the associated modal matrix P and diagonal matrix D, and
use these values to solve the following system differential equations:
* = X1 + 4 x2
*2 = 2 x1 + 3 x2
%3D
Given that whent 0, x, 0 and x2 2.
(b) Use the 4th order Runge Kutta method to solve the differential equation:
dy
e* y
%3D
dx
for values of x = 0 (0.2) 0.4 given that y = 1 when x = 0.
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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