I deducted that we have A1+A2=2.8x10^-3
But I can't seem to relate the other information. Any help ?

 

Depending on the method of solution - say by Laplace's method ['s' domain] or differential equation you have to formulate the particular equation or equations which satisfy the boundary conditions of capacitor voltage and series current. Given there is no source you can readily predict the final value conditions in the circuit.

Which method or methods of solution have you been taught?

 

Write down the equations you know, i.e. the voltage and current relationship of a resistor, inductor, and capacitor.

The inductor current is equal to the capacitor current and the capacitor voltage is the integral of that current.
You should be able to find the values by using the initial conditions, like you did with A1+A2 = 2.8mA

Another option is relating capacitor voltage to the sum of the resistor and inductor voltages.