information:highlighting, structural:summarization, structural:scholar_edition
Examples

In the first group of examples u is an unknown function of x, and c and ω are constants that are supposed to be known. Two broad classifications of both ordinary and partial differential equations consist of distinguishing between linear and nonlinear differential equations, and between homogeneous differential equations and heterogeneous ones.

In the next group of examples, the unknown function u depends on two variables x and t or x and y.