Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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2.2.8. Ordinary
![The differential equation
\[
\frac{d^2y}{dx^2} + 5 \frac{dy}{dx} - 14y = 0
\]
has characteristic equation
\[
\boxed{\phantom{---}} = 0 \quad \text{help (formulas)}
\]
with roots
\[
\boxed{\phantom{---}} \quad \text{help (numbers)}
\]
Therefore, there are two linearly independent solutions
\[
\boxed{\phantom{---}} \quad \text{help (formulas)}
\]
*Note: Enter the solutions as a comma-separated list (they should be those usual exponential ones as in the book).*
Use these to solve the initial value problem
\[
\frac{d^2y}{dx^2} + 5 \frac{dy}{dx} - 14y = 0, \quad y(0) = -7, \quad \frac{dy}{dx}(0) = -2
\]
\[
y(x) = \boxed{\phantom{---}} \quad \text{help (formulas)}
\]](https://content.bartleby.com/qna-images/question/4d6d6ec3-8d2a-4662-b20e-640089acaa34/6ef6c176-863b-42d1-9fea-734df6edd89e/76p6dtt_processed.png)
Transcribed Image Text:The differential equation
\[
\frac{d^2y}{dx^2} + 5 \frac{dy}{dx} - 14y = 0
\]
has characteristic equation
\[
\boxed{\phantom{---}} = 0 \quad \text{help (formulas)}
\]
with roots
\[
\boxed{\phantom{---}} \quad \text{help (numbers)}
\]
Therefore, there are two linearly independent solutions
\[
\boxed{\phantom{---}} \quad \text{help (formulas)}
\]
*Note: Enter the solutions as a comma-separated list (they should be those usual exponential ones as in the book).*
Use these to solve the initial value problem
\[
\frac{d^2y}{dx^2} + 5 \frac{dy}{dx} - 14y = 0, \quad y(0) = -7, \quad \frac{dy}{dx}(0) = -2
\]
\[
y(x) = \boxed{\phantom{---}} \quad \text{help (formulas)}
\]
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