Solve the given initial-value problem. y" + 18y" + 81ly' = 0, y(0) = 0, y'(0) = 1, y"(0) = -16 y(x) =
Solve the given initial-value problem. y" + 18y" + 81ly' = 0, y(0) = 0, y'(0) = 1, y"(0) = -16 y(x) =
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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![Transcription for Educational Website:
---
**Problem Statement**
Solve the given initial-value problem.
\[ y''' + 18y'' + 81y' = 0 \]
**Initial Conditions:**
- \( y(0) = 0 \)
- \( y'(0) = 1 \)
- \( y''(0) = -16 \)
**Solution Format:**
\[ y(x) = \text{[Box for Solution]} \]
---
**Explanation:**
The problem requires solving a third-order linear homogeneous differential equation with constant coefficients and specific initial conditions. The equation provided is:
\[ y''' + 18y'' + 81y' = 0 \]
The solution involves finding a function \( y(x) \) that satisfies both the differential equation and the given initial conditions. The solution format is presented with a placeholder box where \( y(x) \) should be entered once derived.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdd39804f-6d08-4135-954a-c92ac4c2d043%2Fde8ef7a0-f5a9-4079-9248-daed5c329ff7%2F8fa68b_processed.png&w=3840&q=75)
Transcribed Image Text:Transcription for Educational Website:
---
**Problem Statement**
Solve the given initial-value problem.
\[ y''' + 18y'' + 81y' = 0 \]
**Initial Conditions:**
- \( y(0) = 0 \)
- \( y'(0) = 1 \)
- \( y''(0) = -16 \)
**Solution Format:**
\[ y(x) = \text{[Box for Solution]} \]
---
**Explanation:**
The problem requires solving a third-order linear homogeneous differential equation with constant coefficients and specific initial conditions. The equation provided is:
\[ y''' + 18y'' + 81y' = 0 \]
The solution involves finding a function \( y(x) \) that satisfies both the differential equation and the given initial conditions. The solution format is presented with a placeholder box where \( y(x) \) should be entered once derived.
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