Use Laplace transform to find the solution of the IVP2y'+y=0 , y(0)=-3a) f{{left({t}right)}}

babeeb0oL 2021-01-30 Answered

Use Laplace transform to find the solution of the IVP
2y+y=0,y(0)=3
a) f(t)=3e2t
b)f(t)=3et2
c)f(t)=6e2t
d) f(t)=3et2

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Expert Answer

wornoutwomanC
Answered 2021-01-31 Author has 81 answers

Step 1
Given
Use Laplace transform to find the solution of the IVP,
2y+y=0,y(0)=3
step 2
Solution
2y+y=0
Taking Laplace transform on both sides
L(2y)+L(y)=0
2L(y)+L(y)=0
2[ΔL(y)y(0)]+L(y)=0
2ΔL(y)2y(0)+L(y)=0
2ΔL(y)2(3)+L(y)=0
L(y)[2Δ+1]=6
L(y)=62Δ+1
=62(Δ+12)
Y=L1(3Δ+12)=3L1(1Δ+12)
Y(t)=3et2
Therefore the required answer is f(t)=3et2

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