Question

NOT Correct (1 point) Consider the initial value problem y"+16y 48t, y(0)3, /(0)-9. 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). (s 2Y(s)-3s-9)+16Y(s) help (formulas) 48/s 2 b. Solve your equation for Y(s). C{y(t))=48/(s 2(s2+ 16) (3s)(s*2+16)+9/(s^2+16) Y(s) c. Take the inverse Laplace transform of both sides of the previous equation to solve for y(t). (t) -3tsin(6t)+3cos(6t) Note: You can eam partial credit on this problem Preview My Answers Submit Answers Your score was recorded LG

having trouble finding y(t)

Answer 1

Y"+164 = 48t. ;4(0)=3, '(o)=9 . let, l(62)) = FO) Lly!!) = s?F(S) - syeo) - y'(o) ES? F(S) -35-9. - L(Y!! +16 y) = L(48+) = $?F(S) - 35-9 +16 FLs) = 42 7 (5²+16) F (S) = 35+ 9 +48 f(s) = 35776 + 52 (8416) F(S) a 3579 ²+16 s²/ 35 3 [5²716)-52 52(5²+16) S2+ 16 +16 s²+16 sin 4t. “yet) -I'(FCS)) = 3 los 47 +3+ +