The auxiliary equation for our differential equation is:

A.E.

In this case, we have:

(repeated root)

We need to use the second form from the table above (y = e^mx(A + Bx)), and once again use the correct variables (t and i, instead of x and y).

So .

Now to find the values of the constants:

So we can write

So

The graph of our solution is as follows: