At steady state, UC1(+∞) = 66.7vc2 (+∞) = 33.3v according to the capacitance voltage dividing formula.
Equivalent capacitance c series = c1* C2/(c1+C2) = 2 μ f.
Time constant τ=RC= 100*2=2μs
According to the three-factor method, UC1(t) = 66.7+(0-66.7) e (-t/τ).
uc2(t)=33.3+( 100-33.3)e^(-t/τ)