Solving RC Circuits with Switch: Finding Vs(t) and Vc(t)

[frutti]

Homework Statement

i need to find the V_s(t) and V_c(t)

http://img32.imageshack.us/img32/9071/circuiten.jpg

The Attempt at a Solution

since there is a switch i used two cases to find the V_c
one with switch on and switch off
switch on
http://img704.imageshack.us/img704/6180/switchon.jpg
and switch off
http://img265.imageshack.us/img265/3259/switchoff.jpg

but I am lost after this...
help me!

 

[berkeman]

Homework Statement

i need to find the V_s(t) and V_c(t)

http://img32.imageshack.us/img32/9071/circuiten.jpg

The Attempt at a Solution

since there is a switch i used two cases to find the V_c
one with switch on and switch off
switch on
http://img704.imageshack.us/img704/6180/switchon.jpg
and switch off
http://img265.imageshack.us/img265/3259/switchoff.jpg

but I am lost after this...
help me!

The cap still needs to be there with the switch ON.

Write the KCL equation for the node at the top of capacitor (with the bottom of the cap being the common "ground" node), and solve the resulting differential equation, using the initial conditions from when the switch was open (assume the switch is closed at t=0). Show us your work, so we can help you more if you need it.