V2 is 100V. The equation of the voltage across the capacitor is:
Vc = 500(1-exp(-71.429*t))

How do we get this equation? Do I have to remove the dependent source when considering the effect of 100V source? I've tried superposition and this is what I got
vc = 100/((1/1 - e^t/RC) - 0.8) (which is NOT right)

http://img12.imageshack.us/img12/8358/uploada.jpg

Hi,

One way to go about this is to transform the circuit into the frequency domain,
solve for Vc, then transform the resulting equation back into the time domain.
Once in the frequency domain, you can kill each source in turn and equate
for Vc. To get the equation for the current out of G1 you can use a voltage
source of 1v on the input, then before solving for Vc replace G1 with Vc*G1
and of course make G1=0.02.
Once you transform back into the time domain you get the first equation you
gave, except using normal floating point you get -71.42857 (with more digits too)
like this:

Vc=500(1-exp(-71.42857...*t))

If you need more help just yell.

Good luck with it.