How to Solve a First Order Transient Circuit Using Differential Equations?

[RadiationX]

I'm having serious trouble understanding how to solve this problem using the differential equation method ( I MUST use this method). I provided the answer but my solution attempts are not producing the same result.

Here is the problem. http://img102.imageshack.us/img102/4176/testproblembe8.th.jpg

The first thing I need to do is find the voltage across the capacitor at time $$t_{0^-}$$. By combining the 4k and 6k resistors and using voltage division I see that the voltage across the capacitor for $$t_(0^-)= 8V$$

Now I'm confused here, should I also find the current in the circuit for $$t_(0^-)$$?


Let me assume that I don't need this parameter and then I go on the analyze this circuit for $$t_(0^+)$$

For this circuit all we have is one loop consisting of the capacitor and the 4k and 6k resistors.
Now I can write and equation for the current around this loop:
$$C\frac{dV_c(t)}{dt} + 6ki(t)=0$$

 

[Kenny Lee]

Have you tried using a combination of Kirchoff's voltage and current laws? I tried it and got three equations and three unknowns. But its crazy to solve. I doubt its the right way, but maybe you can give it a shot?

How about Laplace transformations? Find the transfer function for capacitor and output, and then inverse laplace it for the final answer.