RC circuit with pulse input voltage; finding the time constants
I did not check your calculations, but I can tell you that this question can be solved much easier: 

The time constant at Y1 is the time constant of a well known and simple RC circuit, which (google tells us) is T=RC with R=Ri+R1 and thus T is 1.2ms.

As the voltage potential at Y2 is always exactly half way between V1 and Y1, the resulting voltage at Y2 is always just a (Y-axis) scaled version of the voltage at Y1. So Y2 must have the same time constant as Y1 which is T=1.2ms.