 A partial differential equation is a differential equation that relates functions of more than one variable to their partial derivatives.Differential equations arise naturally in the physical sciences, in mathematical modelling, and within mathematics itself.For example, Newton's second law, which describes the relationship between acceleration and force, can be stated as the ordinary differential equation
The heat equation in one space variable, which describes how heat diffuses through a straight rod, is the partial differential equation
Here is the temperature of the rod at position and time and is a constant that depends on how fast heat diffuses through the rod.