Question: Why doesn't dsolve produce four linearly independent solutions?

I'm trying to solve a fourth order ODE but for some reason I only end up with three constants at the end. I'm using Maple 16. Here's the code I have been using:

dsolve(diff(x(t), t$4)+4*diff(x(t), t$2)-4*x(t)+1);

The output is 

x(t) = 1/4+_C1*exp(sqrt(-2+2*sqrt(2))*t)+_C2*exp(-sqrt(-2+2*sqrt(2))*t)+_C3*exp(-I*sqrt(2+2*sqrt(2))*t)

When I try to solve the homogeneous equation I get the expected four linearly indep solutions:

x(t) = _C1*exp(-sqrt(-2+2*sqrt(2))*t)+_C2*exp(sqrt(-2+2*sqrt(2))*t)+_C3*exp(-I*sqrt(2+2*sqrt(2))*t)+_C4*exp(sqrt(-2+2*sqrt(2))*t)

Adding 1/4 to this gives me the general solution I would expect, but I don't see why I should need to do this step. I'm at a loss for what I am doing wrong so any help would be greatly appreciated. Thanks in advance.