Okay, applying Kirchhoff's voltage law, we will write the following.

Minus VOC plus Rth times

i + V = 0 then we're

going to substitute in for

the i C dv dt so we have

-Voc+Rth C dv/dt + v = 0.

At this point, we have a differential equation involving the circuit variable v,

but it's not in standard form.

To put it into standard form we need to make the highest

order derivative which is this dv/dt have a unity coefficient and to do that we have

to divide every term by Rth C then we're going to also put this term here

on the other side because it doesn't involve the circuit variable V.

So when we have done that,

we will have dv/dt plus one

over Rth C times V is equal to

one over Rth C times Voc.

That's the differential equation in standard form.

Now we can identify this parameter tau,

which we will find will have particular significance.

It's equal to RthC, and that's worth making a note of.

For the first order RC circuits, the time constant tau is RthC.

Then the K is all of this over here.

And something that will be needing to write the solution is K times tau.

You can see that when you multiply K times tau, the RthC cancels.

And you actually just end up with the Voc.