Determining the voltage and charges across each capacitor
Considering the top circuit :

Applying KCL at the nodes :

A : (Vd - Va) / R1 = ( Va / sC1) + ( (Va - Vb) / sCx)

B : ( (Va - Vb) / sCx ) + ( (Vd - Vb) / sC2) = ( Vb - VL) / R2

L : ( (Vb - VL) / R2 ) = VL / sCL

3 equations for 3 unknowns. 

( Don't forget to put Laplace transform of input ie of Vd).

(Did I miss something ?)