dq1/dt = i(t)

dq2/dt = i(t)

dq1/dt = dq2/dt

q1(t) = q2(t) + Constante

Or q1(0) = Q et q2(0) = 0 --> Constante = Q

q1(t) = q2(t) + Q

q1(t) - q2(t) = Q (constante)
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U1 + U2 = - R.i

q1/C1 + q2/C2 = - R.dq1/dt

q1/C1 + (q1-Q)/C2 = - R.dq1/dt

R.dq1/dt + q1.(1/C1 + 1/C2) = Q/C2

dq1/dt + q1.(C1+C2)/(R.C1.C2) = Q/(R.C2)

q1(t) = Q/(R.C2) * R.C1.C2/(C1+C2) + K.e^(-t * (C1+C2)/(R.C1.C2))

Or q1(0) = Q -->

Q = Q/(R.C2) * R.C1.C2/(C1+C2) + K

Q = Q*C1/(C1+C2) + K

K = Q(1 - C1/(C1+C2)) = Q.C2/(C1+C2)

q1(t) = Q * C1/(C1+C2) + Q . C2/(C1+C2).e^(-t * (C1+C2)/(R.C1.C2))

q2(t) = q1(t) - Q

q2(t) = (Q * C1/(C1+C2) - Q ) + Q . C2/(C1+C2).e^(-t * (C1+C2)/(R.C1.C2))

q2(t) = - Q * C2/(C1+C2) + Q . C2/(C1+C2).e^(-t * (C1+C2)/(R.C1.C2))

Pour t --> +oo : q1 = Q * C1/(C1+C2) et q2 = - Q * C2/(C1+C2)
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Eo = 1/2.Q²/C1

Ef = (1/2).Q² * C1/(C1+C2)² + 1/2 . Q² * C2/(C1+C2)² = (1/2).Q²/(C1+C2)

Delta E = (1/2).Q²/(C1+C2) - 1/2.Q²/C1

Delta E = - Q².C2/(2.C1.(C1+C2))

... indépendant de la valeur de R.
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Sans aucune vérification ... et sans énoncé sous les yeux.