Question

Use Laplace Transform to solve the given initial-value problem. et y'" – 16y y(0) = y"(0) y'(o) 0 = 4

Answer 1

Given equation = et s-1 y" - 16 y' taking Laplace traustorm both side. Lyon - 164'3 = Liet} L{y} - 161 {y} = 처 0 .: L{ $"} = 337(3) 32yco) - 19'(o)-Y"(0) 413) - 45 SY(3) - yco) syls) Putting both in o 83 y(s) – 45 16 5 yy) and L&J'} = = 715) (33-165) = +45 5-1 → 452-45+1 5-1 452-45+1 13-1 (13-16 5) yis) Now taking the inverse Laplace 2 glu) = {"'{432-45+1 13+) (33–163)

LI { 43 - 45 +) SCS-) (+4) (S-+) ~ 1 + 49 96 (-4) { = {ts sts- - ialiste) = {} - I AS - {} {-} 18 49 96 ) 닝t - se - é -4t 49. set 160 + 96