Abstract: Publisher Summary
This chapter focuses on compatible systems. The two equations f(x,y,z,p,q) = 0 and g(x,y,z,p,q) = 0 for z = z(x, y) are said to be compatible if every solution of the first equation is also a solution of the second equation, and conversely. The conditions for consistency of a system of simultaneous partial differential equations of the first order, if the number of equations is an exact multiple of the number of dependent variables involved, is given in Forsyth. Jacobi's method takes a given partial differential equation and creates a compatible equation, and then uses elimination between these two equations. If it is known that a linear homogeneous ordinary differential equation of order n has solutions in common with a linear homogeneous ordinary differential equation of order m (with m < n), then it is possible to determine a differential equation of lower degree that has, as its solutions, these common solutions.
Publication Year: 1992
Publication Date: 1992-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
Access and Citation
AI Researcher Chatbot
Get quick answers to your questions about the article from our AI researcher chatbot