The problem I am having is finding the voltage across the capacitor. I drew it right but my graph is not right. I am thinking my switching configurations are wrong. The problems says the circuit is steady state before the switch closes at t=0. Find v(t) for t >0.

 

You should have your transient analysis start with zero initial values.

I'm not a LTSpice user, so I don't know the specifics.

 

You have not connected the negative side of V1 to GND. Both sides of the capacitor are floating with respect to GND.

Simple NOOB mistake -- we've all done it!

Good Luck

 

That fixed the problem. I get the exp. Curve I was searching.

 

The simplest way to simulate this circuit in the time domain (.TRAN) with C1 starting at zero volts is to dispense with the switch and simply connect V1 directly to the input of the circuit.

To specify the method of simulation and to start with C1 initially discharged, right click anywhere in the schematic.
Select Edit Simulation Command and left click.
Specify how long you want to simulate for ( I suggest 1 s) by putting a value in Stop Time
Check the Start external DC supply voltages at 0V box.

When you run the simulation this way, the simulator first does an initial .DC solution with V1 set to 0V, meaning that C1 winds up with zero volts across it. It then steps V1 to 18V, and then does the Transient simulation run.