Consider the initial value problem λ = ÿ' ÿ(t) = C1 -2 - [8] ÿ, ÿ(0) 0 a. Find the eigenvalue X, an eigenvector ₁, and a generalized eigenvector 2 for the coefficient matrix of this linear system. c. Solve the original initial value problem. y₁(t) = y₂(t): = V₁ H. b. Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers. + C₂ V₂ =
Consider the initial value problem λ = ÿ' ÿ(t) = C1 -2 - [8] ÿ, ÿ(0) 0 a. Find the eigenvalue X, an eigenvector ₁, and a generalized eigenvector 2 for the coefficient matrix of this linear system. c. Solve the original initial value problem. y₁(t) = y₂(t): = V₁ H. b. Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers. + C₂ V₂ =
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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please solve it on paper
![Consider the initial value problem
a. Find the eigenvalue X, an eigenvector ₁, and a generalized eigenvector 2 for the coefficient matrix of this linear system.
λ =
=
-2
✓ = [²32] (₁
ÿ'
ÿ,
ÿ(0) =
0
y(t) = C₁
c. Solve the original initial value problem.
y₁(t) =
=
Y₂(t)
, 1:
=
b. Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers.
V₂:
+ C₂
=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F05295cc1-71f0-4e3b-b6f8-2c1731c6d617%2Fad2b8fa6-524f-4484-8549-a11e9546a7c7%2F7exssdp_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the initial value problem
a. Find the eigenvalue X, an eigenvector ₁, and a generalized eigenvector 2 for the coefficient matrix of this linear system.
λ =
=
-2
✓ = [²32] (₁
ÿ'
ÿ,
ÿ(0) =
0
y(t) = C₁
c. Solve the original initial value problem.
y₁(t) =
=
Y₂(t)
, 1:
=
b. Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers.
V₂:
+ C₂
=
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