We use the following:

and obtain:

After multiplying throughout by 20, we have:

Taking Laplace transform and using the fact that i(0) = 0:

Using Scientific Notebook to find the partial fractions:

So

So

+ cos200t − 2 sin 200t

NOTE: Scientific Notebook can do all this for us very easily. In one step, we have:

+ cos200t − 2 sin 200t

Transient part:

Steady state part: