Find y(t) for the following differential equation using the Laplace transform dy dy +7- + 10y = 6u(t) dt dt2 if y(0) = 0 and dy(0) = 0 dt where (a) u(t) = 3 (b) u(t) = 3t (c) u(t) = 3e-3t %3D
Find y(t) for the following differential equation using the Laplace transform dy dy +7- + 10y = 6u(t) dt dt2 if y(0) = 0 and dy(0) = 0 dt where (a) u(t) = 3 (b) u(t) = 3t (c) u(t) = 3e-3t %3D
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
Please use the below definition of Laplace transform (DO NOT USE TABLE RULES)
F(s) = L[f(t)] = integral from 0 to infinity e^-st*f(t)dt
Please find y(t) using Laplace transform in the picture.
Eg. Integral from 0 to infinity e^(-st) * 1 dt when f(x) = 1.
-st = u
-sdt = du
dt = (1/-s)du
so, (1/-s)integral from 0 to infinity e^u du
= (1/-s)*[{e^-(st)}infinitiy - {e^-(st)}0]
Answer: 1/s
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