RC analysis

I have the circuit whose LTSPICE text is given below. The voltage sources and voltage controlled switches are only there to set the initial voltages on the capacitors. Thus the circuit of interest consists of two capacitors and two resistors.

I've been trying to determine an equation that describes the voltage on C2 as it varies with time, but with my limited mathematical skill, haven't been able to. I end up with differential equations that contain the voltage on C1 as well, in a way that I can't substitute for.

Any thoughts?

Sylvia.

Version 4 SHEET 1 880 680 WIRE 624 16 256 16 WIRE 96 32 0 32 WIRE -48 128 -96 128 WIRE 0 128 0 112 WIRE 576 128 528 128 WIRE 624 128 624 96 WIRE -48 144 -48 128 WIRE 96 144 96 32 WIRE 144 144 96 144 WIRE 256 144 256 16 WIRE 256 144 224 144 WIRE 320 144 256 144 WIRE 576 144 576 128 WIRE 96 208 0 208 WIRE 256 208 96 208 WIRE 368 208 256 208 WIRE 400 208 400 144 WIRE 400 208 368 208 WIRE 544 208 528 208 WIRE 576 208 576 192 WIRE 576 208 544 208 WIRE -96 224 -96 208 WIRE -64 224 -96 224 WIRE -48 224 -48 192 WIRE -48 224 -64 224 WIRE 400 256 400 208 WIRE 624 256 624 208 WIRE 624 256 400 256 FLAG 368 208 0 FLAG -64 224 0 FLAG 544 208 0 SYMBOL cap 80 144 R0 SYMATTR InstName C1 SYMATTR Value 10 SYMBOL cap 240 144 R0 SYMATTR InstName C2 SYMATTR Value 300 SYMBOL res 240 128 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R1 SYMATTR Value 0.5 SYMBOL res 416 128 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R2 SYMATTR Value 1 SYMBOL sw 0 112 R0 SYMATTR InstName S1 SYMATTR Value SW1 SYMBOL voltage 0 16 R0 WINDOW 123 0 0 Left 2 WINDOW 39 0 0 Left 2 SYMATTR InstName V1 SYMATTR Value 50 SYMBOL voltage -96 224 R180 WINDOW 0 24 96 Left 2 WINDOW 3 24 16 Invisible 2 WINDOW 123 0 0 Left 2 WINDOW 39 0 0 Left 2 SYMATTR InstName V2 SYMATTR Value PULSE(-1 1 0 0 0 1 2 1) SYMBOL sw 624 112 R0 SYMATTR InstName S2 SYMATTR Value SW1 SYMBOL voltage 528 224 R180 WINDOW 0 24 96 Left 2 WINDOW 3 24 16 Invisible 2 SYMATTR InstName V3 SYMATTR Value PULSE(-1 1 0 0 0 1 2 1) SYMBOL voltage 624 0 R0 WINDOW 123 0 0 Left 2 WINDOW 39 0 0 Left 2 SYMATTR InstName V4 SYMATTR Value 1 TEXT -412 232 Left 2 !.tran 50 TEXT -368 328 Left 2 !.model SW1 SW(Ron=0.0001)