I just got back a test from lecture last week where one of the questions asks to find the time constant when the circuit has a dependent voltage source of 0.5k*ix and 2 resistors each 2k Ohm. My answer is 40ms but it got marked wrong.

Any help tackling this problem or showing me my error would be greatly appreciated.

Here's the picture redrawn for clarity.

Keep in mind that I make the assumption that this circuit is in DC steady state and this is not stated in the problem.

My logic from the picture in text goes like this.

The term ix = 0 because the cap is an open circuit. This makes the dependent source = 0, therefore the middle branch is a short and the resistance seen by the cap is 2k ohm. RC = 2k Ohm * 20 micro Farads.