Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y"+5y=2t^2-9 , y(0)=0 , y'(0)=-3

ankarskogC 2021-09-17 Answered

Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below.
y"+5y=2t29,y(0)=0,y(0)=3

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Expert Answer

Aubree Mcintyre
Answered 2021-09-18 Author has 73 answers

y"+5y=2t29
y(0)=0,y(0)=3
L{y"}+sL{y}=L{2t29}
s2Y(s)sy(0)y(0)+5Y(s)=L{2t2}L{9}
=4s39s
s2Y(s)sy(0)+3+5Y(s)=4s39s
Y(s)[s2+5]=4s39s3
Y(s)=4s39s3s2+5=49s23s3s3(s2+5)
y(t)=L1{49s23s3s3(s2+5)}
=2t2535sin(5t)5+49cos(5t)254925
[L1{49s23s3s3(s2+5)}=45s315s(s2+25)+49s25(25+52)4925s2]
2t2549253525sin(5t)+4925cos(5t)

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