Consider the following initial value problem: 1 y" + 8y' + 15y = d(t – 5) + u10(t); y(0) = 0, y'(0) : 4 a) Find the solution y(t). y(t) = u(t) + Ua(t) where c = and d =
Consider the following initial value problem: 1 y" + 8y' + 15y = d(t – 5) + u10(t); y(0) = 0, y'(0) : 4 a) Find the solution y(t). y(t) = u(t) + Ua(t) where c = and d =
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:
\[ y'' + 8y' + 15y = \delta(t - 5) + u_{10}(t); \quad y(0) = 0, \quad y'(0) = \frac{1}{4} \]
a) Find the solution \( y(t) \).
\[ y(t) = \boxed{\phantom{\text{solution}}} + \left( \boxed{\phantom{\text{expression}}} \right) u_c(t) + \left( \boxed{\phantom{\text{expression}}} \right) u_d(t) \]
where \( c = \boxed{\phantom{\text{value}}} \) and \( d = \boxed{\phantom{\text{value}}} \).
b) Use a graphing utility to plot the solution \( y(t) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd4bdfca1-c479-4089-8b74-947c8fb213c2%2Fb817b2cb-e3fe-4907-b597-1f12a43fcc31%2F86b97ac_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the following initial value problem:
\[ y'' + 8y' + 15y = \delta(t - 5) + u_{10}(t); \quad y(0) = 0, \quad y'(0) = \frac{1}{4} \]
a) Find the solution \( y(t) \).
\[ y(t) = \boxed{\phantom{\text{solution}}} + \left( \boxed{\phantom{\text{expression}}} \right) u_c(t) + \left( \boxed{\phantom{\text{expression}}} \right) u_d(t) \]
where \( c = \boxed{\phantom{\text{value}}} \) and \( d = \boxed{\phantom{\text{value}}} \).
b) Use a graphing utility to plot the solution \( y(t) \).
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