With this method what we are trying to do is guess an appropriate Yp by looking at the right hand side of the equation.
In this case, we have
So an appropriate Yp would be
But let us note that the characteristic equation
Has the roots
Therefore we must select a multiple of Yp because with our initial guess we will get an equation that does not work. So let us guess
Solve to find C. There is no need to have A, B and C!
Edit- Like HallsofIvey pointed out, we have 2 roots that are identical (I should have noticed!) so we need a Yp of the form