i solved it upto Y"+Y'+Y= 0. it can be solved using the general second order DE solution steps. But the problem is the Right hand side of the equation. How to solve that part? I mean how to find the Particular Integral ..... The answer for the first part of is
Yc=e^(-0.5x) (Acos(root(3)/2) + B sin (root(3)/2) )
my problem again is as to how to find the Particular integral