Laplace transform:

1.)

(a) Consider the integral in the time domain: Use the definition of the Laplace transform and integration by parts to find: (b) Use your result from above to find the Laplace transform of dy + y(0) = K u(t) + y(0) = 10) =0 Ta (c) find the ratio: Y(a) U (s) as a function of a.Use the method of Laplace transforms to solve the initial value problem: dy dy dy + 5 di2 + 6y(#) = 7; dt =0; #(0) = 1 dt