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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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