Nonclassical Contact Symmetries and Charpit’s Method of Compatibility

Charpit’s method of compatibility and the method of nonclassical contact symmetries for first order partial differential equation are considered. It is shown that these two methods are equivalent as Charpit’s method leads to the determining equations arising from the method of nonclassical contact symmetries. Several examples are considered illustrating how Charpit’s method leads quickly and easily to nonclassical contact symmetries.