Now

To solve this, we need to work in voltages, not current.

We start with .

The voltage across a capacitor is given by .

It follows that .

So for this example we have:

Substituting known values:

Then

Taking Laplace:

Since , we have:

So, taking inverse Laplace

NOTE: For the part: , we use:

So we have:

Solution Using Scientific Notebook

1. To find the Inverse Laplace:

2. To solve the original DE:

Exact solution for v(t):

To see what this means, we could write it as follows:

To see what our expression for v(t) means, we graph it as follows: