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Problem #8: Consider the following initial value problem. 0 1 ≤ 3 3 < t < 5 0 5 <1 00 Problem #8(a): Problem #8(b): Problem #8(c): Problem #8(d): y' + 6y 11 Problem #8(e): y(0) = 7 (a) Find the Laplace transform of the right hand side of the above differential equation. (b) Let y(t) denote the solution to the above differential equation, and let Y((s) denote the Laplace transform of y(t). Find Y(s). (c) By taking the inverse Laplace transform of your answer to (b), the solution y(t) can be written in the form f(t) U(t-3)+g (t) U(t-5)+ h(t). Enter the function f(t) into the answer box below. (d) Referring to part (c) above, enter the function g(t) into the answer box below. (e) Referring to part (c) above, enter the function h(t) into the answer box below. Enter your answer as a symbolic function of s, as in these examples Enter your answer as a symbolic function of s. as in these examples Enter your answer as a symbolic function of t, as in these examples Enter your answer as a symbolic function of t, as in these examples. Enter your answer as a symbolic function of t, as in these Cxamples

Problem #8: Consider the following initial value problem. 0 1 ≤ 3 3 < t < 5 0 5 <1 00 Problem #8(a): Problem #8(b): Problem #8(c): Problem #8(d): y' + 6y 11 Problem #8(e): y(0) = 7 (a) Find the Laplace transform of the right hand side of the above differential equation. (b) Let y(t) denote the solution to the above differential equation, and let Y((s) denote the Laplace transform of y(t). Find Y(s). (c) By taking the inverse Laplace transform of your answer to (b), the solution y(t) can be written in the form f(t) U(t-3)+g (t) U(t-5)+ h(t). Enter the function f(t) into the answer box below. (d) Referring to part (c) above, enter the function g(t) into the answer box below. (e) Referring to part (c) above, enter the function h(t) into the answer box below. Enter your answer as a symbolic function of s, as in these examples Enter your answer as a symbolic function of s. as in these examples Enter your answer as a symbolic function of t, as in these examples Enter your answer as a symbolic function of t, as in these examples. Enter your answer as a symbolic function of t, as in these Cxamples

Advanced Engineering Mathematics
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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Problem #8: Consider the following initial value problem. Problem #8(a): Problem #8(b): Problem #8(c): Problem #8(d): y' +6y= Problem #8(e): 0 1 ≤ 3 11 3 < t < 5 0 5 ≤ 100 y(0) = 7 (a) Find the Laplace transform of the right hand side of the above differential equation. (b) Let y(t) denote the solution to the above differential equation, and let Y((s) denote the Laplace transform of y(t). Find Y(s). (c) By taking the inverse Laplace transform of your answer to (b), the solution y(t) can be written in the form f(t) U(t-3)+g (t) U(t-5)+ h(t). Enter the function f(t) into the answer box below. (d) Referring to part (c) above, enter the function g(t) into the answer box below. (e) Referring to part (c) above, enter the function h(t) into the answer box below. Enter your answer as a symbolic function of s, as in these examples Enter your answer as a symbolic function of s. as in these. examples Enter your answer as a symbolic function of t, as in these examples Enter your answer as a symbolic function of t, as in these examples Enter your answer as a symbolic function of t, as in these examples
Transcribed Image Text:Problem #8: Consider the following initial value problem. Problem #8(a): Problem #8(b): Problem #8(c): Problem #8(d): y' +6y= Problem #8(e): 0 1 ≤ 3 11 3 < t < 5 0 5 ≤ 100 y(0) = 7 (a) Find the Laplace transform of the right hand side of the above differential equation. (b) Let y(t) denote the solution to the above differential equation, and let Y((s) denote the Laplace transform of y(t). Find Y(s). (c) By taking the inverse Laplace transform of your answer to (b), the solution y(t) can be written in the form f(t) U(t-3)+g (t) U(t-5)+ h(t). Enter the function f(t) into the answer box below. (d) Referring to part (c) above, enter the function g(t) into the answer box below. (e) Referring to part (c) above, enter the function h(t) into the answer box below. Enter your answer as a symbolic function of s, as in these examples Enter your answer as a symbolic function of s. as in these. examples Enter your answer as a symbolic function of t, as in these examples Enter your answer as a symbolic function of t, as in these examples Enter your answer as a symbolic function of t, as in these examples
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