Capacitor charge time on DC RLC circuit

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Homework Statement

Inductor, resistor and a capacitor is connected to a DC source in series.
DC source is 220 V
Capacitance is 10F
Inductance 5H
Resistor 22 ohm
Vc(0) = 50V

Question is asking for the charge time of the capacitor, when it gets charged fully and then it starts to act like open circuit (If I'm not mistaken it must be act like short until gets fully charged and then acts like open circuit)

Homework Equations

The Attempt at a Solution

I wrote down the KVL and equation. And then replaced the VL with L.dI/dt and I=C.dVc/dt
Finally I ended up with a dif. equation on Vc.

However, I couldn't proceed any further.

 

[rude man]

The Attempt at a Solution

I wrote down the KVL and equation. And then replaced the VL with L.dI/dt and I=C.dVc/dt
Finally I ended up with a dif. equation on Vc.

However, I couldn't proceed any further.

Why not? What was your equation?