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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
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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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

Find y(t) for the following differential equation using the Laplace transform dy dy +7- dt + 10y = 6u(t) dt2 if y(0) = 0 and dy(0) %3D dt where (а) и(t) — 3 (b) u(t) = 3t (c) u(t) = 3e-3t
Transcribed Image Text:Find y(t) for the following differential equation using the Laplace transform dy dy +7- dt + 10y = 6u(t) dt2 if y(0) = 0 and dy(0) %3D dt where (а) и(t) — 3 (b) u(t) = 3t (c) u(t) = 3e-3t
Expert Solution
Step 1

The given differential equation is:

d2ydx2+7dydx+10y=6u(t) ;          y(0)=0,    y'(0)=0

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