Consider the following initial value problem: y" + 11y' + 28y = 8(t – 5) + u10(t); y(0) = 0, y (0) -) Find the solution y(t). y(t) : ua(t where c= and d = ) Use a graphing utility to plot the solution y(t).
Consider the following initial value problem: y" + 11y' + 28y = 8(t – 5) + u10(t); y(0) = 0, y (0) -) Find the solution y(t). y(t) : ua(t where c= and d = ) Use a graphing utility to plot the solution 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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![Consider the following initial value problem:
\[ y'' + 11y' + 28y = \delta(t - 5) + u_{10}(t); \quad y(0) = 0, \quad y'(0) = \frac{1}{4} \]
a) Find the solution \( y(t) \).
\[ y(t) = \]
\[
\quad + \left( \quad \right) u_c(t)
\]
\[
\quad + \left( \quad \right) u_d(t)
\]
where \( c = \_\_ \) and \( d = \_\_ \)
b) Use a graphing utility to plot the solution \( y(t) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdddd00a4-d31c-4cdf-9a7a-3406e89ad378%2F9ffaf9a3-86f1-472f-bb8b-71367c69cf8a%2Fya9rsff_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the following initial value problem:
\[ y'' + 11y' + 28y = \delta(t - 5) + u_{10}(t); \quad y(0) = 0, \quad y'(0) = \frac{1}{4} \]
a) Find the solution \( y(t) \).
\[ y(t) = \]
\[
\quad + \left( \quad \right) u_c(t)
\]
\[
\quad + \left( \quad \right) u_d(t)
\]
where \( c = \_\_ \) and \( d = \_\_ \)
b) Use a graphing utility to plot the solution \( y(t) \).
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