The differential equation - 7-17 - 9y = 0 has characteristic equation = 0 help (formulas) with roots Note: Enter the roots as a comma separated list. Therefore there are three fundamental solutions help (formulas) Note: Enter the solutions as a comma separated list. Use these to solve the initial value problem y(x) d³y dx³ help (numbers) ¸ď²y dy 17. dx dx² 7. - 9y = 0, y(0) = -2, help (formulas) dy dx -(0) -9, == d²y 22 (0) = 7 10 dx²
The differential equation - 7-17 - 9y = 0 has characteristic equation = 0 help (formulas) with roots Note: Enter the roots as a comma separated list. Therefore there are three fundamental solutions help (formulas) Note: Enter the solutions as a comma separated list. Use these to solve the initial value problem y(x) d³y dx³ help (numbers) ¸ď²y dy 17. dx dx² 7. - 9y = 0, y(0) = -2, help (formulas) dy dx -(0) -9, == d²y 22 (0) = 7 10 dx²
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
2.3.6. Ordinary
![The differential equation
\[ \frac{d^3y}{dx^3} - 7 \frac{d^2y}{dx^2} - 17 \frac{dy}{dx} - 9y = 0 \]
has characteristic equation
\[
\boxed{\phantom{\text{solution}}}=0 \quad \text{help (formulas)}
\]
with roots
\[
\boxed{\phantom{\text{roots}}} \quad \text{help (numbers)}
\]
*Note: Enter the roots as a comma-separated list.*
Therefore, there are three fundamental solutions
\[
\boxed{\phantom{\text{solutions}}} \quad \text{help (formulas)}
\]
*Note: Enter the solutions as a comma-separated list.*
Use these to solve the initial value problem
\[
\frac{d^3y}{dx^3} - 7 \frac{d^2y}{dx^2} - 17 \frac{dy}{dx} - 9y = 0, \quad y(0) = -2, \quad \frac{dy}{dx}(0) = -9, \quad \frac{d^2y}{dx^2}(0) = 7
\]
\[ y(x) = \boxed{\phantom{\text{y(x)}}} \quad \text{help (formulas)} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4d6d6ec3-8d2a-4662-b20e-640089acaa34%2Fb89685fd-f257-48f3-a60b-1d6a5f9a09fa%2F7iz8v8g_processed.png&w=3840&q=75)
Transcribed Image Text:The differential equation
\[ \frac{d^3y}{dx^3} - 7 \frac{d^2y}{dx^2} - 17 \frac{dy}{dx} - 9y = 0 \]
has characteristic equation
\[
\boxed{\phantom{\text{solution}}}=0 \quad \text{help (formulas)}
\]
with roots
\[
\boxed{\phantom{\text{roots}}} \quad \text{help (numbers)}
\]
*Note: Enter the roots as a comma-separated list.*
Therefore, there are three fundamental solutions
\[
\boxed{\phantom{\text{solutions}}} \quad \text{help (formulas)}
\]
*Note: Enter the solutions as a comma-separated list.*
Use these to solve the initial value problem
\[
\frac{d^3y}{dx^3} - 7 \frac{d^2y}{dx^2} - 17 \frac{dy}{dx} - 9y = 0, \quad y(0) = -2, \quad \frac{dy}{dx}(0) = -9, \quad \frac{d^2y}{dx^2}(0) = 7
\]
\[ y(x) = \boxed{\phantom{\text{y(x)}}} \quad \text{help (formulas)} \]
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