Finding current, power and energy for a 2.5mH inductor with sinusoidal voltage

[TSizzle55]

Homework Statement

The voltage across an L = 2.5mH inductor is v(t) = 10 cos(1000t)mV, with i(0) = 1 mA.
(a) Find i(t) for t ≥ 0.
(b) Find the power and energy.

Homework Equations

V= L * di/dt
Power= V * i
V * i= L * i * (di/dt)

The Attempt at a Solution

I really don't know where to start. I'm just looking for an explanation of what the problem is asking (What does 'Find the power and energy' mean?). That would be really helpful, thanks.

 

[Astronuc]

The power is the rate at which energy changes or the rate at which it is supplied or stored.

In DC, power is pretty straightforward. P = VI, and V and I are constant.

In AC, V and I are varying with time and out of phase depending on the reactance in the circuit/component.

Presumably one's textbook describes voltage, current and power with respect to an inductor and AC.

Given V(t) = L * di/dt, how would one find i(t) if one knows v(t)?