Electric field with constant direction

[Grieverheart]

I just started Classical Electrodynamics and stumbled upon a problem:

An electric field has this form:

$$E_{x}=ax ,E_{y}=0 ,E_{z}=0$$

where a is a constant.Find the density of the charge(ok that's easy).How do you explain that the field points towards a constant direction although the density of the charge is homogene?

Ok,so I though maybe the charged body is like mug with infinite thickness and an infinite height.Is this correct?Is there a way to find the answer mathematically?

 

[Meir Achuz]

The charge density is constant, but the solution to the PDE div E=a is not unique.
The solution for E also depends on the boundary conditions.
In this case the BC as x, y, and -->infinity determines E.