I'm interested in knowing the formula which represents the voltage across the 10 ohm resistor. I know that it's going to be the current multiplied by the resistance, which means I have to find the current passing through the 10 ohm resistor as a function of time. I also know that when the capacitor is fully charged, the voltage across will stop changing (and as i = C dv/dt, the current will go to zero also). This means that from this time on, it's just a series resistor circuit.
However, before this time, how would you find the voltage across the 10 ohm resistor? Is the solution general for non constant input voltage?