TABLE OF CONTENTS The general form of a differential equation with one energy storage element is given in Equation 4.1.
Where y is the output and x is the input to the system.
Removing the input source at time t = 0, the input x becomes zero at t ? 0, and the differential equation becomes
We will assume a solution of exponential form
Selecting a value of 
satisfies Equation 4.1.
The coefficient A can be solved using the initial condition of the system, and for that let's work through an example. The capacitor C = 1 uF in Figure 4.2 was initially charged with voltage V 0. At time t = 0, the switch was thrown in the position of the resistor R = 1 k, essentially removing the power source from the system. For the circuit component as given, we will determine the voltage as a function of time after the capacitor is connected with the resistor and also find the discrete time solution of the network for the sampling rate of 10 samples per second.
Assume at t = 0 the switch was thrown towards the resistor. Applying the Kirchoff's voltage law on the RC network, we get a first order differential...
