Solve the initial value problem below using the method of Laplace transforms. y"-8y'+41y=29e^{2t} ,y(0)=1 , y'(0)=7

ediculeN 2021-09-16 Answered

Solve the initial value problem below using the method of Laplace transforms.
y8y+41y=29e2t
y(0)=1,y(0)=7

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Expert Answer

Neelam Wainwright
Answered 2021-09-17 Author has 102 answers

The given IVP is
y8y+41y=29e2t
y(0)=1,y(0)=7
Taking Laplace in both side we get
L[y]8L[y]+41L[y]=29L[e2t]
s2y(s)sy(0)y(0)8(sy(s)y(0))+41y(s)=29s2
(s28s+41)y(s)s(1)78(1)=29(s2)
(s28s+41)y(s)s7+8=29(s2)
(s28s+41)y(s)s+1=29(s2)
(s28s+41)y(s)=29(s2)+s1
(s28s+41)y(s)=29+s23s+2(s2)
y(s)=s23s+31(s2)(s28s+41)
y(s)=s23s5s+5s+31+1010(s2)(s28s+41)
y(s)=s28s+5s+4110(s2)(s28s+41)
y(s)=(s28s+41)+5(s2)
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