Question

(1 point) Consider the initial value problem 4y 8t, y(0) 4, y'(0) 3. f 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 othe other (until you get to part (b) below). Take the Laplace transform one side of the equation help (formulas) b. Solve your equation for Y(8) Y(s) C{y(t) = Take the inverse Laplace transform of both sides of the previous equation to solve for y(t) y(t)

Answer 1

aing Japloa tan fom 4 8 人lt) Aly 1= +4 YIS)& s2 Y(s)- Us-3 +4 Y(S 8 2 S4) Y(S)4s-3 (b) (tu) Y(S) 45+3 + S2 8tus8+35 Y (s) S(st4 ust358 2 (ntes)s t

By Paatial faction 4S+3548 Cs+D us3t 3s+8=ASIst)t Bls+44 CS+D) s Es44B+CSDs 2 AS+4AS+ ust3s+ (A+)s(B+D) s+4 As +uB AtC=4 B+D 3 A O 2 C = 4-0 D 3-9 C =4 D= us+1 + 2 Y(S)= Taking invease Japlace Toofoor + 22 at +4 cos (2t) +LSint)