Question

please help

(1 point) Use the Laplace transform to solve the following initial value problem: y" + y = 0, y(0) = 1, y'(0) = 1 (1) First, using Y for the Laplace transform of y(t), i.e., Y = L(y(0), find the equation you get by taking the Laplace transform of the differential equation to obtain (2) Next solve for Y = (3) Finally apply the inverse Laplace transform to find y(t) y(t) =

Answer 1

Answers y" ty=0 ,y (0)=2 , y(0)=1 A8, Lly"(t)) = 8²Y(s) - $4(0)-yllo) L (YLt)) = Y(8) putting in given diffrential ean Lly"Lt) & Lly(t) = Llo) B²Y(6) - 89 102-y'(o) +Y(0)=0 (8²+1) Y (8) -8-1=0 Y(6) = stt 82+1 Applying Laplace invorse transform L()) - 1 ) = ( 1 ) y(t) = sint & cost po 4 liat) = sinat & Lt ( a ) = cosat)