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dr = x – y +t dt dy =エ+3y +t+1 dt (20, yo) = (-4, 5)

dr = x – y +t dt dy =エ+3y +t+1 dt (20, yo) = (-4, 5)

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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Solve the initial value problem given by dr = x – y+t dt - fhip dt -r + 3y +t+1 (Lo, Yo) = (-4, 5)
Transcribed Image Text:Solve the initial value problem given by dr = x – y+t dt - fhip dt -r + 3y +t+1 (Lo, Yo) = (-4, 5)
Expert Solution
Step 1

Given that,

dxdt=x-y+tdydt=x+3y+t+1

This can be written by,

X'=1-113X+tt+1

Now the homogenous eigen value is,

(1-λ)(3-λ)+1=03-λ-3λ+λ2+1=0λ2-4λ+4=0(λ-2)2=0

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