Here I am trying to find the input current I(t) and Vc(t).
From my calculation, it's evident that Vc(0+)=Vc(0-)=0V and Vc(∞)= 10V but I am confused about the first capacitor. When t=0, it acts like a voltage source of 10V but does it supply current to the 2nd capacitor? The second capacitor was shorted when t=0+,then I(t) was flowing through it. Hence,I(0+)=10V/5kohm=2mA.also I am confused about the time constant of the circuit. According my assumption, C1 acts like an independent voltage source from t=0- to t=∞. Then would the time constant be (5*2)=10? Is my assumption correct?