Partial differential equations
Partial differential equations Brent J. Lewis, ... Andrew A. Prudil, in Advanced Mathematics for Engineering Students , 2022 Definitions A partial differential equation is an equation containing an unknown function of two or more variables and its partial derivatives with respect to these variables. The order of a partial differential equations is that of the highest-order derivatives. For example, ∂ 2 � ∂ � ∂ � = 2 � − � is a partial differential equation of order 2. A solution of a partial differential equation is any function that satisfies the equation identically. A general solution is a solution that contains a number of arbitrary independent functions equal to the order of the equation. A particular solution is one that is obtained from the general solution by a particular choice of arbitrary functions. For example, the general solution of the partial differential equation ∂ ...