Solve: y''' — 5y'' — y' + 5y = 0 y(0) -6, y'(0) y(t) = = = 16, y''(0) = - 78
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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![The task is to solve the following differential equation with given initial conditions:
\[
y''' - 5y'' - y' + 5y = 0
\]
**Initial Conditions:**
- \( y(0) = -6 \)
- \( y'(0) = -16 \)
- \( y''(0) = -78 \)
The solution should take the form:
\[
y(t) = \_\_
\]
This involves finding a function \( y(t) \) that satisfies both the differential equation and the initial conditions. This is a third-order linear homogeneous differential equation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F15c022aa-6711-4b29-ab7f-4e5d70ca82f7%2Fd297bdd3-6131-4441-abd3-83ef1db382df%2Fx65fuzt_processed.png&w=3840&q=75)
Transcribed Image Text:The task is to solve the following differential equation with given initial conditions:
\[
y''' - 5y'' - y' + 5y = 0
\]
**Initial Conditions:**
- \( y(0) = -6 \)
- \( y'(0) = -16 \)
- \( y''(0) = -78 \)
The solution should take the form:
\[
y(t) = \_\_
\]
This involves finding a function \( y(t) \) that satisfies both the differential equation and the initial conditions. This is a third-order linear homogeneous differential equation.
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