Q1) Solve and plot the following system of ordinary differential equations: x'(t) = x(t)-2y(t) + z(t) y'(t) = -x(t) - z(t) z'(t)=-4x(t)+4y(t) - 5z(t) The initial conditions, x (0) =1, y (0) =2, z (0) =3 t = [0,3]
Q1) Solve and plot the following system of ordinary differential equations: x'(t) = x(t)-2y(t) + z(t) y'(t) = -x(t) - z(t) z'(t)=-4x(t)+4y(t) - 5z(t) The initial conditions, x (0) =1, y (0) =2, z (0) =3 t = [0,3]
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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![Q1) Solve and plot the following system of ordinary differential equations:
x'(t) = x(t) - 2y(t) + z(t)
y'(t) = -x(t) - z(t)
z'(t)=-4x(t) +4y(t) - 5z(t)
The initial conditions, x (0) =1, y (0) =2, z (0) =3
t = [0,3]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe7e1366b-e899-4587-a55b-0443c6362745%2Fb93f7d08-37ef-4018-94d4-25c32bb68e64%2Fuxhrf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Q1) Solve and plot the following system of ordinary differential equations:
x'(t) = x(t) - 2y(t) + z(t)
y'(t) = -x(t) - z(t)
z'(t)=-4x(t) +4y(t) - 5z(t)
The initial conditions, x (0) =1, y (0) =2, z (0) =3
t = [0,3]
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Step 1: Introduction
VIEWStep 2: Calculating eigenvalues of the coefficient matrix
VIEWStep 3: Calculating eigenvector of matrix A corresponding to -1
VIEWStep 4: Calculating eigenvector of matrix A corresponding to -2
VIEWStep 5: Calculating eigenvector of matrix A corresponding to -3
VIEWStep 6: Calculating particular solution of the given system
VIEWStep 7: Plotting the solution
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