Those are not easy to find but it is clear that neither 0 nor 2i is a root so you need to look for a "particular solution" of the form
y= Acos(2x)+ Bsin(2x)+ Cx^2+ Dx+ E
Here the characteristic equation is . Again, that has only irrational roots which will be hard to find but we know the "particular solution" must be of the formy''' + y' - 5y = 4sinx + 2x^2
Are you sure you have copied the problems correctly? It looks to me like the general solution to either of those will be very hard to find.