It has me completely stumped because the usual equation for the transient response of a capacitor assumes the circuit has a voltage source, not a current source, and requires a value for the time constant, which is normally defined as \$ RC \$. If there were a resistor in parallel with the current source, I could use Thevenin's theorem to get the equivalent circuit with a voltage source and resistor in parallel. But this circuit has no resistor.
What's the correct way to approach modeling the voltage over the capacitor as a function of time? My thought was that I could just assume the current source isn't ideal and add a resistor in series with it, to represent its internal resistance. But even then, I still wouldn't have a value for the initial voltage to plug into the usual capacitor voltage equation, since I wouldn't have a specific value for the resistance of the current source, so I don't see how I could get a numerical time value for part b.