ABSTRACT
Differential equations are used extensively in physics. The laws of physics can often be expressed compactly using the differential equation notation. The differential equation model is particularly useful for understanding two properties of systems — resonance and state. The state of a system describes the information stored in the system. This chapter provides two simple examples of systems which can be described by differential equations — radioactive decay and a mass on a spring. Differential equations are used in radiology in those areas where radiology and physics intersect. The solutions to a differential equation when the input is zero are called the natural solutions. The solution to a differential equation which is due to the input is called the forced solution or nonhomogeneous solution. The eigenfunctions of a differential equation are signals which pass through the system unchanged except possibly for a change in scale.
