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:

If we assume that at t=0, vC(0)=0, and that the inhomogeneous differential equation that governs vC is dVc/dt +vC/CR = vS/CR:

Find the solution for vC to the homogeneous part of this equation (dVc/dt +vC/CR =0). Please use 'K' for any constant of integration you find ...