Consider the special case of the RLC circuit in which the resistance is negligible and t...

Consider the special case of the RLC circuit in which the resistance is negligible and the driving EMF is

zero. The differential equation governing the charge on the capacitor in this case is

If the capacitor has an initial charge of q₀ coulombs, and no current is flowing initially, determine the charge on the capacitor for t > 0, and the corresponding current in the circuit. [Hint: Let u = dq/dt and use the chain rule to show that this implies du/dt = u(du/dq).]