Initial Value Problems

Abstract

Consider a simple RC circuit such as the one shown in Fig. 12.1. Kirchhoff’s law states that this circuit can be modelled by the following equation:

$$ \frac{dV}{dt}=-\frac{V(t)}{RC} $$

This model would be easy to use if the voltage and the values of the resistor and capacitor are known. But what if the voltage is not known or measurable over time, and only the initial conditions of the system are known? That is to say, only the initial value of the voltage and of its derivative, along with the resistor and capacitor value, are known.