Solve the given initial value problem. y'' +4y' +29y=0; y(0) = 2, y'(0) = -1 y(t) =
Solve the given initial value problem. y'' +4y' +29y=0; y(0) = 2, y'(0) = -1 y(t) =
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
![The problem presented is an initial value problem for a second-order linear differential equation. It is expressed as follows:
Solve the given initial value problem:
\[ y'' + 4y' + 29y = 0; \quad y(0) = 2, \quad y'(0) = -1 \]
There is a box provided to fill in the solution for \( y(t) \).
Explanation:
We are given a homogeneous linear differential equation with constant coefficients. The task is to find the function \( y(t) \) that satisfies the differential equation and the initial conditions.
- The equation is of the form \( y'' + 4y' + 29y = 0 \).
- Initial conditions are specified as \( y(0) = 2 \) and \( y'(0) = -1 \).
The solution involves finding the characteristic equation, solving for the roots, and using these roots to construct the general solution. Finally, apply the initial conditions to find the specific coefficients for the solution \( y(t) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa827acfe-a0bc-46c0-ab61-62657df3b5db%2Ff486a5ab-b6ed-4a11-9245-bc10fd644434%2Fv00iklb_processed.png&w=3840&q=75)
Transcribed Image Text:The problem presented is an initial value problem for a second-order linear differential equation. It is expressed as follows:
Solve the given initial value problem:
\[ y'' + 4y' + 29y = 0; \quad y(0) = 2, \quad y'(0) = -1 \]
There is a box provided to fill in the solution for \( y(t) \).
Explanation:
We are given a homogeneous linear differential equation with constant coefficients. The task is to find the function \( y(t) \) that satisfies the differential equation and the initial conditions.
- The equation is of the form \( y'' + 4y' + 29y = 0 \).
- Initial conditions are specified as \( y(0) = 2 \) and \( y'(0) = -1 \).
The solution involves finding the characteristic equation, solving for the roots, and using these roots to construct the general solution. Finally, apply the initial conditions to find the specific coefficients for the solution \( y(t) \).
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