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Q3. (a) If Ax= 1 x, determine the eigenvalues and the corresponding eigenvectors for A = ) 4 Herce, 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 X2 = 2 x1 + 3 x2 Given that when t = 0, x1 = 0 and x2 = 2. (b) Use the 4h order Runge Kutta method to solve the differential equation: dy = e* y dx for values of x = 0 (02) 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.

Q3. (a) If Ax= 1 x, determine the eigenvalues and the corresponding eigenvectors for A = ) 4 Herce, 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 X2 = 2 x1 + 3 x2 Given that when t = 0, x1 = 0 and x2 = 2. (b) Use the 4h order Runge Kutta method to solve the differential equation: dy = e* y dx for values of x = 0 (02) 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.

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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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,
Transcribed Image Text: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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