For this system of 1st order ODE, y₁' = 4y₁ +2y₂ −2e-²t Y₂'= 3y₁ +3y₂ + 3e¯²¹ € 1:66.
For this system of 1st order ODE, y₁' = 4y₁ +2y₂ −2e-²t Y₂'= 3y₁ +3y₂ + 3e¯²¹ € 1:66.
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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I need detailed explanation solving this problem (2.c) from Engineering Mathematics, please.
Transcribed Image Text:2. For this system of 1st order ODE,
y₁' = 4y₁ +2y₂ −2e-2¹
Y2'= 3y₁ +3y₂ + 3e¯²¹
(a) Find the homogeneous solution of the above systems of differential equations.
(b) Find the particular solution using "method of undetermined coefficient."
(c) Find the particular solution using "method of variation of parameters."
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Step 1: Write the given system
VIEWStep 2: Write the given system in matrix form and determine the eigenvalues of A
VIEWStep 3: Determine the corresponding eigenvector for the eigenvalue 1
VIEWStep 4: Determine the corresponding eigenvector for the eigenvalue 6 and write the complement function
VIEWStep 5: Take a particular solution of the system using the fundamental matrix
VIEWStep 6: Determine the particular solution
VIEWStep 7: Determine the required particular solution of the system
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