solve the initial value problem with using laplace Y'+3Y=6e^{-3t}cos 6t+24 Y(0)=0

Yulia 2020-12-16 Answered
solve the initial value problem with using laplace
Y+3Y=6e3tcos6t+24
Y(0)=0
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Expert Answer

casincal
Answered 2020-12-17 Author has 82 answers

Step 1
The given IVP is as follows.
Y+3Y=6e3tcos6t+24
Y(0)=0
Apply Laplace transform on both sides of the given differential equation as follows.
LY+3Y=L6e3tcos6t+24
LY+3Y=L6e3tcos6t+L24
sLYY(0)+3LY=6Le3tcos6t+L24
(s+3)LY=6s+3(s+3)2+62+24s
LY=6(s+3)2+62+24s(s+3)
LY=6(s+3)2+62+8s8(s+3)
Step 2
Apply inverse Laplace transform on both sides as follows.
L1{L{Y}}=L1{6(s+3)2+62+8s8(s+3)}
Y(t)=L1{6(s+3)2+62}+8L1{1s}8L1{1(s+3)}
Y(t)=e3tsin6t+88L1{1(s+3)}

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