Question

5(10pt). Use Laplace transform to solve the equation

$BcJHj1JE3PfcgAAAABJRU5ErkJggg==$ $kfb7PcgtMvVaUAAAAASUVORK5CYII=$

Answer 1

Solue + Given differential equation in X+ X= 0 X 60)= 0 , X'10) = 0 , *"(0) = 1 Taking Laplace of both sides, we get L{x}+x} = 0 - 0 Since -MX10) - AXO) - X"o) = s?x19) -1 and L{x} = n(A) This equation o becomes - Ax4) - 1 + X(S) = 0 or +1) =

oy x6 = molti XW) - s3+1 Taking inverse Laplace of oth sides, we get X125 = 1"{x191} = 114 otti Since "Kamil = F"condsato 1. By using partial decomposition, we get t"{m} = {{!( wt + 127 erl] 2

(7) : 7 + ( ) بمر - م - solution is - required Thus (1) 2 17 : ( ما بعد * - * = ** | For mala Land (ht ) بود مهم : { منه )1 (in ( ht م م ={جام داده } مهم = اما
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