8

Solve the initial value problem below using the method of Laplace transforms. y" - y' - by = 0, y(0) = - 2, y'(0) = 19 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. y (t) = (Type an exact answer in terms of e.) Table of Laplace Transforms X i Properties of Laplace Transforms X f (t) F(s) = Eff(t)} { {f + g} = =[f) + fig) { {cf) = cf (f) for any constant c 1 (f) (s) = si [f)(s) - f(0) I (f' ) (s) = s2 1(f)(s) - sf(0) - f'(0) E (f() ) (s) = s" eff)(s) - s" - 1f(0) - s -2f'(0) - ... - f(n - 1)(0) 1 e at s - a * 1( F 1 + F 2 ) = 2" " ( F 1 ) + 1" (F 2 ) n! { { CF ) = Cf ' {F) to , n = 1,2,... k sin kt 52 +12: 520 Print Done S cos kt Print Done