Write the homogeneous part of the differential equation system, namely f(x)= g(x)=0 in the normal form, obtained in the 1st photo, and solve the resulting system using eigen-values and eigen-vectors.
Write the homogeneous part of the differential equation system, namely f(x)= g(x)=0 in the normal form, obtained in the 1st photo, and solve the resulting system using eigen-values and eigen-vectors.
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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Question
Write the homogeneous part of the
![L¡ = D – 2
L2 = D – 1
L3 = -2D + 1
L4 = -D – 1
f (x) =
g (x) = x? + 3x – 1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F86158032-ed7c-43a3-b5cc-df6a415b87b0%2F562a7911-78ee-40b3-870a-a38200b04412%2Fqrknnuj_processed.png&w=3840&q=75)
Transcribed Image Text:L¡ = D – 2
L2 = D – 1
L3 = -2D + 1
L4 = -D – 1
f (x) =
g (x) = x? + 3x – 1
![u'(x) + v'(x) – 2u(x) – v(x) –1/x= 0
(-2u'(x) – v(x)+ u(x)– v(x)– x² – 3x+1 =0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F86158032-ed7c-43a3-b5cc-df6a415b87b0%2F562a7911-78ee-40b3-870a-a38200b04412%2Fmhv55bf_processed.png&w=3840&q=75)
Transcribed Image Text:u'(x) + v'(x) – 2u(x) – v(x) –1/x= 0
(-2u'(x) – v(x)+ u(x)– v(x)– x² – 3x+1 =0
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