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Laplace Transform Technics 13. Find the Laplace transform of x(t), L[x(t)]. 2(t)+3(t)+x(t) = 5, x(0) = 2, ȧ(0) = -1 s'X-5%- x. } +3 {58-x} + & 2s+7 28278 (A) (D) 282 +381 282 +381 (25²+35+ 1) = 2827s+5 (B) s(28² + 38+1) ((E). 482 +48 +5 s(2s2+38+1) 281 (C) -82+5 28238 +1 (F) s(282 +381) 14. Find the inverse Laplace transform of the fol- lowing function. 382+2 X(s) = 83+82 +48 +4 X = 5/3 ון = = 5/5 +25% +2% +370 45-2 +6 45²+45 +5 S 45²+45+5 5(25435+1) (A)e-t +2 cos(2t) sin(2t)

Laplace Transform Technics 13. Find the Laplace transform of x(t), L[x(t)]. 2(t)+3(t)+x(t) = 5, x(0) = 2, ȧ(0) = -1 s'X-5%- x. } +3 {58-x} + & 2s+7 28278 (A) (D) 282 +381 282 +381 (25²+35+ 1) = 2827s+5 (B) s(28² + 38+1) ((E). 482 +48 +5 s(2s2+38+1) 281 (C) -82+5 28238 +1 (F) s(282 +381) 14. Find the inverse Laplace transform of the fol- lowing function. 382+2 X(s) = 83+82 +48 +4 X = 5/3 ון = = 5/5 +25% +2% +370 45-2 +6 45²+45 +5 S 45²+45+5 5(25435+1) (A)e-t +2 cos(2t) sin(2t)

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please explain this in depth question 13 only and there is work done on the right but i dont really understand it. why on the right hand side does 5 turn into 5/s what makees that happen. just one specific question i hope u can explain along with the rest of the problem 

Laplace Transform Technics 13. Find the Laplace transform of x(t), L[x(t)]. 2(t)+3x(t)+x(t) = 5, x(0) = 2, x(0) = == 2s+7 (A) 2s² + 38 +1 (D) 28278 2s238 +1 2s²+7s+5 4s² +48 +5 (B) s(2s2+381) ((E) s(2s² + 3s+1) 2s+1 (C) -s²+5 2s2+381 (F) s(2s² +381) -1 14. Find the inverse Laplace transform of the fol- lowing function. X(s) = 3s2+2 (A)e-t +2 cos(2t) - sin(2t) $3 + s² +48 +4 2 { s² - ≤ x - x. } + 3 { ≤8-x} 2{5'8- + x = 5/5 (25²+35+ 1) = 5+25x+2% P ✗= ון ין = 5/3 + +3% 45-2 +6 45²+45+5 S 45²+45+5 5(25435+1)
Transcribed Image Text:Laplace Transform Technics 13. Find the Laplace transform of x(t), L[x(t)]. 2(t)+3x(t)+x(t) = 5, x(0) = 2, x(0) = == 2s+7 (A) 2s² + 38 +1 (D) 28278 2s238 +1 2s²+7s+5 4s² +48 +5 (B) s(2s2+381) ((E) s(2s² + 3s+1) 2s+1 (C) -s²+5 2s2+381 (F) s(2s² +381) -1 14. Find the inverse Laplace transform of the fol- lowing function. X(s) = 3s2+2 (A)e-t +2 cos(2t) - sin(2t) $3 + s² +48 +4 2 { s² - ≤ x - x. } + 3 { ≤8-x} 2{5'8- + x = 5/5 (25²+35+ 1) = 5+25x+2% P ✗= ון ין = 5/3 + +3% 45-2 +6 45²+45+5 S 45²+45+5 5(25435+1)
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