Applications of Second-Order Differential Equations

In this section, a few applications of the theory and methods that were previously outlined will be illustrated. However, it should be noted that a substantial percentage of the application of second (and higher) order ordinary differential equations is in association with solving partial differential equations, a topic discussed in Chapter 6. 

As in Section 2.4, some problem setup as well as solution techniques will be demonstrated. Eor example, consider the following problem in heat transfer through a cylindrical conductor [15]. 

Two concentric cylindrical metallic shells are separated by a solid material. If the two metal surfaces are maintained at different constant temperatures, what is the steady-state temperature distribution within the separating material  

In this problem, temperature, T, and the heat flow per unit area, Q, depend on the radius, r. Then if we consider the condition of the system about an element of thickness, Ar and with the aid of Eigure 3.1, the important quantities can be organized according to the procedure of Section 2.4. Therefore, 

FIGURE 3.1 Radial heat flow through cylindrical conductor. 

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