Are you familiar with Variation of Parameters?.
Because 1 has multiplicity 2, we have:
Integrate the last two and get:
So, put them together with and get
The complimentary function after solving the auxiliary equation is:
How should I start finding out the particular integral?
y= k(e^x)(cosx) ( where only k is a constant)
or y= k(e^p.x)(cos q.x) ( where k, p and q are constants)