Use Laplace transform to solve the folowing initial value problem y"+2y'+2y=0 y(0)=2 y'(0)=-1

chillywilly12a 2020-12-24 Answered
Use Laplace transform to solve the folowing initial value problem y"+2y+2y=0
y(0)=2
y(0)=1
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Expert Answer

berggansS
Answered 2020-12-25 Author has 91 answers
Step 1Given y"+2y+2y=0
y(0)=2
y(0)=1Taking Laplace transform on both sidesL{y"}+2L{y}+2L{y}=0
s2y(s)sy(0)y(0)+2[sy(s)y(0)]+2y(s)=0
giveny(0)=2
y(0)=1
s2y(s)2s+1+2[sy(s)2]+2y(s)=0
[s2+2s+2]y(s)2s3=0
y(s)=2s+3s2+2s+2Step 2L1y(s)=L1{2s+3s2+2s+2}
=L1{2s+1(s+1)2+1+11(s+1)2+1}
=2L1{s+1(s+1)2+1}+L1{1(s+1)2+1}
y(t)=2etcost+etsint
y(t)=2etcost+etsint
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