Page "Partial differential equation" Paragraph 15

where c is any constant value.

These two examples illustrate that general solutions of ordinary differential equations ( ODEs ) involve arbitrary constants, but solutions of PDEs involve arbitrary functions.

A solution of a PDE is generally not unique ; additional conditions must generally be specified on the boundary of the region where the solution is defined.

For instance, in the simple example above, the function f ( y ) can be determined if u is specified on the line x