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2. For the system of equations: dx = a11x + a12y, dt dy a21x + az2y. dt First, review lecture notes to see how we eliminate one variable to arrive at a single second-order equation. Then find the characteristic equation and solve the eigenvalues of the equation. Once x(t) is found, y(t) can be found by setting 1 dx - a11x) y(t)= (a12 # 0) a12 dt By using the above method, find solutions for the following systems: (a) dx = -4x + y, dt dy = 3x. dt

2. For the system of equations: dx = a11x + a12y, dt dy a21x + az2y. dt First, review lecture notes to see how we eliminate one variable to arrive at a single second-order equation. Then find the characteristic equation and solve the eigenvalues of the equation. Once x(t) is found, y(t) can be found by setting 1 dx - a11x) y(t)= (a12 # 0) a12 dt By using the above method, find solutions for the following systems: (a) dx = -4x + y, dt dy = 3x. dt

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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2. For the system of equations: dx = aj|x + a12y, dt dy a21x + az2y. dt First, review lecture notes to see how we eliminate one variable to arrive at a single second-order equation. Then find the characteristic equation and solve the eigenvalues of the equation. Once x(t) is found, y(t) can be found by setting 1 dx - a11x) y(t) = (a12 # 0) a12 dt By using the above method, find solutions for the following systems: (a) dx = -4x + y, dt dy = 3x. dt (b) dx = 2x – 3y, dt %3! dy = x- 2y. dt
Transcribed Image Text:2. For the system of equations: dx = aj|x + a12y, dt dy a21x + az2y. dt First, review lecture notes to see how we eliminate one variable to arrive at a single second-order equation. Then find the characteristic equation and solve the eigenvalues of the equation. Once x(t) is found, y(t) can be found by setting 1 dx - a11x) y(t) = (a12 # 0) a12 dt By using the above method, find solutions for the following systems: (a) dx = -4x + y, dt dy = 3x. dt (b) dx = 2x – 3y, dt %3! dy = x- 2y. dt
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