First, we find the Laplace Transform of each term in the equation:

`sI-i(0)+2I+5 I/s=1/s`

We multiply throughout by s and use the fact that i(0) = 0 to obtain:

`s^2I+2sI+5I=1`

Solving for I and completing the square on the denominator:

`I=1/(s^2+2s+5)` `=1/((s+1)^2+4)` `=1/2 2/((s+1)^2+4)`

Taking the inverse Laplace transform to give us the current as a function of time:

`i=1/2e^(-t)sin 2t`

Easy to understand math videos:
MathTutorDVD.com