Consider solving an equation like (5.1) but with nonzero initial conditions.
(a) Write the corrected form of (5.2), writing the transfer function in factored form as indicated just after (5.2). Consider the extra terms in Y which arise from the initial conditions; show that the inverse transforms of such terms can always be found from L6, L7, L8, and L18.
(b) Find the explicit form of the inverse transform of the transfer function for a=b (use L7), and so write the general solution of (5.2) with nonzero initial conditions as a convolution integral plus the terms which you found in (a).