Capacitor discharging into another capacitor with RC timing

[cupid.callin]

1. The problem statement and my attempt
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Its not the correct answer.
answer is: Q/2(1 - e^-2t/RC)

 

[gneill]

Use conservation of charge; there's nowhere for it to escape to!

 

[ehild]

The sum of the voltages across R and C2 is equal to the voltage of the first capacitor. Q1/C1 =I*R +Q2/C2. As the charge is conserved, Q1+Q2=Qo=const, and I=dQ2/dt=-dQ1/dt, so you have the differential equation (Qo-Q2)C1+Q2/C2+RdQ2/dt=0 with the initial condition Q2(0)=0.

ehild