Chapter 8.6, Problem 21P

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 $(6.15)]$.

$5y^{\prime \prime }+6y^{\prime }+2y=x^2+6x$