Use the Laplace transform to solve the following initial value problem: 2y"+4y'+17y=3cos(2t) y(0)=y'(0)=0 a)take Laplace transform of both sides of th

smileycellist2 2021-02-08 Answered
Use the Laplace transform to solve the following initial value problem:
2y"+4y+17y=3cos(2t)
y(0)=y(0)=0
a)take Laplace transform of both sides of the given differntial equation to create corresponding algebraic equation and then solve for L{y(t)}b) Express the solution y(t) in terms of a convolution integral
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Expert Answer

opsadnojD
Answered 2021-02-09 Author has 95 answers
Step 1
Given differntial equation is,
2y"+4y+17y=3cos(2t)
y(0)=y(0)=0
L[y"]=s2L{y(t)}sy(0)y(0)
L[y]=sL{y(t)}y(0)
L[cos(at)]=ss2+a2
Taking Laplace transform of equation (1),
2L[y"]+4L[y]+17L[y]=3L[cos(2t)]
s2L{y(t)}sy(0)y(0)+4[sL{y(t)}y(0)]+17L{y(t)}=3L{cos(2t)}
s2Ly(t)+4sLy(t)+17Ly(t)=3xss2+4
(s2+4s+17)L{y(t)}=3ss2+4
a)L{y(t)}=3ss2+4×1s2+4s+17
b)y(t)=0t[3cos(3w)]×[e2tsin13w]dw
This is required Laplace transform.
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