Given the RC circuit below, where the voltage source is providing a square wave with a low level of 0 V and a high level of 1 V as shown on the plot below:

Find the homogeneous differential equation that describes the voltage over the capacitor (vC). A homogeneous DE will have the form dy/dx +y.f(x) = 0, and can be found from an equation of the form dy/dx +y.f(x) = g(x) by setting g(x)=0.

The governing KCL for this circuit is C.dvC/dt = (vS-vC)/R.

An example solution might look like: dVc/dt - C/Vc = 0