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Consider the following system of differential equations dx + 3x – y = 0, dt dy + 10x – 4y = 0. dt а) Write the system in matrix form and find the eigenvalues and eigenvectors, to obtain a solution in the form (;) = ) 1 C1 Y1 1 + C2 ebt %3| Y2 where C1 and C2 are constants. Give the values of A1, Y1, A2 and that A1 < d2. Y2. Enter your values such Y1 = Y2 Input all numbers as integers or fractions, not as decimals. b) Find the particular solution, expressed as x (t) and y(t), which satisfies the initial conditions x(0) = 4, y(0) = 17. æ(t) = y(t) = ||

Consider the following system of differential equations dx + 3x – y = 0, dt dy + 10x – 4y = 0. dt а) Write the system in matrix form and find the eigenvalues and eigenvectors, to obtain a solution in the form (;) = ) 1 C1 Y1 1 + C2 ebt %3| Y2 where C1 and C2 are constants. Give the values of A1, Y1, A2 and that A1 < d2. Y2. Enter your values such Y1 = Y2 Input all numbers as integers or fractions, not as decimals. b) Find the particular solution, expressed as x (t) and y(t), which satisfies the initial conditions x(0) = 4, y(0) = 17. æ(t) = y(t) = ||

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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Consider the following system of differential equations dæ + 3x – y = 0, dt dy + 10x – 4y = 0. dt a) Write the system in matrix form and find the eigenvalues and eigenvectors, to obtain a solution in the form (;)- ebt Y2 edit + C2 Y1 where C1 and C2 are constants. Give the values of A1, Y1, 2 and y2. Enter your values such that A1 < A2. Y1 = Y2 Input all numbers as integers or fractions, not as decimals. b) Find the particular solution, expressed as x (t) and y(t), which satisfies the initial conditions x(0) = 4, y(0) = 17. x(t) = y(t) = ||
Transcribed Image Text:Consider the following system of differential equations dæ + 3x – y = 0, dt dy + 10x – 4y = 0. dt a) Write the system in matrix form and find the eigenvalues and eigenvectors, to obtain a solution in the form (;)- ebt Y2 edit + C2 Y1 where C1 and C2 are constants. Give the values of A1, Y1, 2 and y2. Enter your values such that A1 < A2. Y1 = Y2 Input all numbers as integers or fractions, not as decimals. b) Find the particular solution, expressed as x (t) and y(t), which satisfies the initial conditions x(0) = 4, y(0) = 17. x(t) = y(t) = ||
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