RC Circuit/Node voltage question

[RED119]

Homework Statement

Homework Equations

The Attempt at a Solution

So you need to find the voltage across node D while the capacitor is charging, so it is going to be related to the voltage of the capacitor, so a function of time, so you need to come up with the equation for Vc(t), which I did. Then you do voltage division to find the voltage of Vb, which would be (Rb/(Ra+Rb))(Vc(t), then to find the voltage on node D you just need to use KVL and add Vb and Vc(t). But this doesn't simplify down to the expression it should be equal to, so there has to be some gap in my reasoning or something.

 

[BvU]

I (think I) see you work it out in terms of $V_C$ which isn't very useful in this case.
The expression for $V_C(t)$ looks good to me. Now add $IR_B$

 

[RED119]

I (think I) see you work it out in terms of $V_C$ which isn't very useful in this case.
The expression for $V_C(t)$ looks good to me. Now add $IR_B$

I have Vb or voltage drop across Rb from (Rb/(Ra+Rb))(Vc(t), and I am adding that to Vc(t), but that isn't correct

 

[BvU]

Oh ?