Chapter 18 Question (Equation 18.55)

I asked the professor about this, but it still did not make sense to me.

I do not see how you go from equation 18.55 to equation 18.56.

when I take the Laplace of equation 18.55 I get:
L*s*ig(s)= vg(s)-d'(s)*V

now I thought V is a constant. How do I get rid of the vg(s) term, and put the equation in the form of ig(s)/d(s) = V/(s*L) ????????????

thanks
Mark