We typically would want a real expression for this, so we may do the following:
and we may replace the two arbitrary constants A and B with two new arbitrary constants:
(What would happen here if you solved the problem using the original exponent form is that A and B would end up being complex constants.)
So a = 3 and b = -3, giving
I wasn't sure... Are you asking for help with the particular solution as well? Or do you have a handle on that?