I'm going through a worked example and am stumped by a certain step.

Having applied the Laplace transform to each term in the original equation, I get the following:

τ [ s * Vc(s) - Vc(0) ] + Vc(s) = Vs(s)

How is this equation rearranged to give:

Vc(s) = Vc(0) / (s+ 1/τ) + Vs(s) / τ(s+1/τ)

?

I can't see how to get from the first equation to the second.

Any help appreciated

 

Just solve for Vc(s)!

 

Break down the parentheses, isolate the terms containing Vc and regroup them. What more is there to say?