RC Circuit Transient Response
@ThePhoton provides the clearest path it seems.  I worked it by hand with Laplace and simulated it in ATP.  When applying superposition you will notice that the impact on Vx from the left side capacitor is exactly negative of the right side capacitor, they cancel.  Thus, only the contribution from the step u(t) shows up in the closed form Laplace solution.  Here are plots of Vx. Top plot is from simulation.  Bottom plot is from MathCAD (used it to get the inverse Laplace).



Here is a plot of all 3 voltages of interest together: