Please fill the blanks.(..... is a blank). Consider the initial value problem y’’+9y=g(t),y(0)=0;y’(0)=0 Where g(t)=t -> if 0<=t<2 g(t)=0 -> if 0<=t<∞ A.Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y(t) by Y(s) . Do not move any terms from one side of the equation to the other (until you get to part (b) below).
Please fill the blanks.(..... is a blank). Consider the initial value problem y’’+9y=g(t),y(0)=0;y’(0)=0 Where g(t)=t -> if 0<=t<2 g(t)=0 -> if 0<=t<∞ A.Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y(t) by Y(s) . Do not move any terms from one side of the equation to the other (until you get to part (b) below).
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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Please fill the blanks.(..... is a blank).
Consider the initial value problem
y’’+9y=g(t),y(0)=0;y’(0)=0
Where g(t)=t -> if 0<=t<2
g(t)=0 -> if 0<=t<∞
A.Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of
y(t) by Y(s)
. Do not move any terms from one side of the equation to the other (until you get to part (b) below).
……………………….=……………..
B.Solve your equation for Y(s).
Y(s)=L(s)=………………………
C.Take the inverse Laplace transform of both sides of the previous equation to solve for
y(t).If necessary ,use h(t)to denote Heaviside function h(t)=0 -> if t<0 or
h(t)=1 -> if 0<=t.
y(t)=…………………….
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