The Invariants of the Linear Partial Differential Equation of the Second Order in two Independent Variables

1912 ◽  
Vol s2-10 (1) ◽  
pp. 406-422
Author(s):  
J. E. Campbell
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Linear Partial Differential Equation ◽  
Second Order ◽  
Partial Differential ◽  
Independent Variables ◽  
Two Independent Variables

On a Linear Partial Differential Equation of Hyperbolic Type

1922 ◽  
Vol 41 ◽  
pp. 76-81
Author(s):  
E. T. Copson
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Linear Partial Differential Equation ◽  
Second Order ◽  
Hyperbolic Type ◽  
Order Partial Differential Equation ◽  
Sound Waves ◽  
Partial Differential ◽  
Method Of Solution ◽  
Image Position

Riemann's method of solution of a linear second order partial differential equation of hyperbolic type was introduced in his memoir on sound waves. It has been used by Darboux in discussing the equationwhere α, β, γ are functions of x and y.

scholarly journals Memoir on the integration of partial differential equations of the second order in three independent variables, when an intermediary integral does not exist in general

1898 ◽  
Vol 62 (379-387) ◽  
pp. 283-285
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
General Feature ◽  
Partial Differential ◽  
First Order ◽  
Independent Variables ◽  
Dependent Variables ◽  
Two Independent Variables

The general feature of most of the methods of integration of any partial differential equation is the construction of an appropriate subsidiary system and the establishment of the proper relations between integrals of this system and the solution of the original equation. Methods, which in this sense may be called complete, are possessed for partial differential equations of the first order in one dependent variable and any number of independent variables; for certain classes of equations of the first order in two independent variables and a number of dependent variables; and for equations of the second (and higher) orders in one dependent and two independent variables.

scholarly journals Different forms of Euler’s theorem forhomogeneous functions to solve partial differential equation

2021 ◽  
Vol 12 (2) ◽  
pp. 2810-2813
Author(s):  
Amit Kumar, Et. al.
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Partial Differential ◽  
Independent Variables ◽  
Euler’S Theorem ◽  
Different Order ◽  
Two Independent Variables

In this paper we will discuss Euler’s theorem for homogenous functions to solve different order partial differential equations. We will see that how we can predict the solution of partial differential Equation using different approaches of this theorem. In fact we also consider the case when more than two independent variables will be involved in the partial differential equation whenever dependent functions will be homogenous functions. We will throw a light on one method called Ajayous rules to predict the solution of homogenous partial differential equation.

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