3 ) consider the following Second order liveer ordinary differential equations y" (t ) - y'(6) - 24 (t) - 81-3 for t20 & #$3. where 8 ( t ) is the Dirac delta function and y (0)= 1 , y'(0)=2. ( 10 marks ) 30) Let Y (S ) be the laplace transform of y (t ). By applying laplace transform to the differential equation , show that Y (S ) = _ S + c -3s - + (s+1) (5-2) 3 e (s+1 ) (S-2) where C is a constant. ( Hint ; J fff(t) ] = - as 2 if (t ) ] 3 b ) Hence, determine ylt) by applying inverse laplace transform to Y ( s )