![]() Only the simplest differential equations are solvable by explicit formulas however, many properties of solutions of a given differential equation may be determined without computing them exactly. Mainly the study of differential equations consists of the study of their solutions (the set of functions that satisfy each equation), and of the properties of their solutions. ![]() Such relations are common therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. Heat is being generated internally in the casing and being cooled at the boundary, providing a steady state temperature distribution. ![]() Visualization of heat transfer in a pump casing, created by solving the heat equation.
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