Question

Homework 16: Problem 3 Previous Problem Problem List Next Problem (1 point) Consider the initial value problem y" + 16y = 64t, y(0) = 9, y'(0) = 6. a. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y(t) by Y(s). Do not move any terms from one side of the equation to the other (until you get to part (b) below). help (formulas) b. Solve your equation for Y(s). Y(s) = L {y(t)} = c. Take the inverse Laplace transform of both sides of the previous equation to solve for y(t). y(t) =

Answer 1

y" Rby : Gut 14909.59 19 603 36 d{4"} + 16d{y} <d{b44} . s? Y68) - sym) -y(0)+1664659) = hehe g?yes) - 95 6 + 1648) una 468){ 408%+14] -95-6 let 44 er godt til #60n] = d' enton] *** peting de leur entre 59 o 8² (52716) 64 ' aps (8416) + 2, (52+6) + s} (asstan) ag=0,92=4, 49 50 s'{*}-strue} = ut - sinut (+ d'{lse}=t '{%$+a2y = sinat)

oderne] + {c} =98's no 3 +68' store 59 cosut + 6xy, sinut o acosyt + 314 sinut ( tran) - Sinat) 4t-8?n4t +96054t +31, sinyt. 964 ) = y(t) = 4t of 9losut + 16 Sin 4t :