Consider the following initial value problem: y" - 4y' - 21y = sin(2t) y(0) = -1, y'(0) = 2 Using Y for the Laplace transform of y(t), i.e., Y = Cty(t) } find the equation you get by taking the Laplace transform of the differential equation and solve for Y(s) =Given y'_ Ayl - 214 = Bin(24 ) -1 (1 ) . y 10 ) = - 1 , y'(ol = 2 we know that + (y "' ) = 524 - sy (o) - y'(0 ) and 2 (y' ) = sy - y ( o ) Now , both sides Lapdance transformation of egh ,is- I (y " - Ay ' - 214 ) =16 in ( 27 ) ] 3 ) 2 (y " ) - 42(y') 212 ( 4 ) = 2 : + ( binat ] = q 5 2+4 5 2 + 92 7 1 ( 52 4 - 5 y (0 ) - y' (0 1 ) - 4 ( sy - y (0) ) - 214 =2 3) 527 - S ( - 1 ) - 2 - 45%- 10= 2 - 214 5 2+ 4 7 ( 3 2-45 - 21 / 4 (. S- 3) 5 274 =) ( 32- 4 5 - 2 1 ) 7 = 2 - (5 - 3) (52 + 4 ) $2+4 2) (5 2 - 45 - 21) y = 2-(53+45-352 - 12) 52+4 ( 5 3 - 352 + 45 )+ 14 ) ( 52+ 4 ) (52-45-21 1