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Problem #6: Consider the following initial value problem. 0 1≤3 y'+3y= 12 3≤1<7 07≤1<% y(0) - 2 (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 transf y(t). Find Y(s). (c) By taking the inverse Laplace transform of your answer to (b), the solution y(7) can be written in th f(t) U(t-3)+g (1) U(t-7)+ h(t). Enter the function f(r) into the answer box below.

Problem #6: Consider the following initial value problem. 0 1≤3 y'+3y= 12 3≤1<7 07≤1<% y(0) - 2 (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 transf y(t). Find Y(s). (c) By taking the inverse Laplace transform of your answer to (b), the solution y(7) can be written in th f(t) U(t-3)+g (1) U(t-7)+ h(t). Enter the function f(r) into the answer box below.

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 #6: Consider the following initial value problem. 0 1≤3 y+3y 12 3≤1<7 07≤1< ∞ y(0) = 2 (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 transf 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 th f(t) U(t-3)+g (t) U(t - 7) + 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.
Transcribed Image Text:Problem #6: Consider the following initial value problem. 0 1≤3 y+3y 12 3≤1<7 07≤1< ∞ y(0) = 2 (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 transf 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 th f(t) U(t-3)+g (t) U(t - 7) + 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.
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