1. Solve the initial value problem: y" - 6y' +9y = 11e³x 21 43 y (0): = 1/2/2 -, y'(0) = 2' == = 2. Find the general solution using VARIATION OF PARAMETERS: D(D+3)y=t(5+ e¹) 3. Solve Ax = x' Eigenvectors and eigenvalues for A 0 A = -2 1 λ₂ = -3i, v₂ 0-2 2 0 4 + 3i A₁ = 3i, v₁ = -2 + 6i, = -17 23 = 0,03 = 4 - 3i -2-6i, 5 21
1. Solve the initial value problem: y" - 6y' +9y = 11e³x 21 43 y (0): = 1/2/2 -, y'(0) = 2' == = 2. Find the general solution using VARIATION OF PARAMETERS: D(D+3)y=t(5+ e¹) 3. Solve Ax = x' Eigenvectors and eigenvalues for A 0 A = -2 1 λ₂ = -3i, v₂ 0-2 2 0 4 + 3i A₁ = 3i, v₁ = -2 + 6i, = -17 23 = 0,03 = 4 - 3i -2-6i, 5 21
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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Transcribed Image Text:1. Solve the initial value problem:
y" - 6y' +9y = 11e³x
21
43
y (0):
= 1/2/2
-, y'(0) =
2'
==
=
2. Find the general solution using VARIATION OF PARAMETERS:
D(D+3)y=t(5+ e¹)
3. Solve Ax = x'
Eigenvectors and eigenvalues for A
0
A = -2
1
λ₂ = -3i, v₂
0-2
2 0
4 + 3i
A₁ = 3i, v₁ = -2 + 6i,
=
-17
23 = 0,03
=
4 - 3i
-2-6i,
5
21
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