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I am reviewing the use of the Laplace Transform to do circuit analysis and I am slightly confused about the transform of a constant voltage source.

For example, lets say we have a constant voltage source V1(t) applied to a circuit for a long time - lets say it reaches steady state. We then apply a step function voltage V2(t) some place else in the circuit while V1(t) is left on.

What is the S-domain equivalent of this circuit? How do you handle the constant voltage source V1(t)? It's not a step response - I have looked all over and I have found nothing on this.

Thanks