Chapter 8.6, Problem 19P

Find the general solution of the following differential equations (complementary function + particular solution). Find the particular solution by inspection or by (6.18), (6.23) or $(6.24).$ Also find a computer solution and reconcile differences if necessary, noticing especially whether the particular solution is in simplest form [see (6.26) and the discussion after (6.15)].

$\left(4D^2+4D+5\right)y=40e^{-3x/2}\sin 2x$