It will take some work, bu here follow the solution for the first problem. We can rewrite the DE like follows
we firstly consider the homogenous part
which has roots at r=3 and r=1
so we know the solution to the homogenous DE and can write it as follows
now we will take the right hand side into account. Since the right hand side of the DE includes one of the terms we find in the homegenous solutions we need to regard the following terms
if you now plug this into the DE and group the terms with the same x you can determine the constants A, B and C. I found them to be respectively 1, 0 and 1. Then finally for the general solution you just combine everything in the following way
and use the initial conditions to solve for the remaining constants
The second problem will require some more work but you could attack it in the same way by first finding the solution of the homogenous DE and afterward incorporating the right hand side.