Or if we're not given those things, then we can derive them

by DC analysis prior to t=0, and use their continuity properties.

But even if you have these, we are not done,

we have to find that derivative and this usually requires circuit analysis.

Here's a simple example, the series RLC circuit.

Find the initial conditions for the solution for v(t).

Suppose we were given v(0+) and i,

i being the current through the inductor at times 0+.

However, because we are trying to find the initial conditions for

the solution for v(t), this is not all we need.

We have one part of it, but we need the derivative of v(0+).

So we can use i = C dv dt, and

then solve for dv dt at 0+.

And that will give us 1 over C times i(0+) which we are given.

This is a harder example.

We will determine the initial conditions needed for v(t),

t greater than or equal to 0, assuming the circuit is at rest,

that is, DC steady state, prior to t=0.

To do this, we should consider what this circuit looks like prior to t=0.

There are four things that we need to consider.