We can write the DE in i and q as follows (call it Equation (1)):

Differentiating gives a 2nd order DE in i:

Auxiliary equation:

,

Solution is:

So

(This means at t = 0, i = A = 0 in this case.)

So

We need to find the value of B.

Differentiating gives:

At t = 0,

Returning to equation (1):

Now, at time t = 0,

So

So B = 19.

Therefore,

SNB Solution:

We need to set it up in terms of q only, to give us a DE which SNB can solve:

To get i, we simply differentiate: