Page 276 - DMTH504_DIFFERENTIAL_AND_INTEGRAL_EQUATION

Richa Nandra, Lovely Professional University Unit 18: Charpit s Method for Solving Partial Differential Equations

Unit 18: Charpit s Method for Solving Partial Notes
Differential Equations

CONTENTS
Objectives
Introduction
18.1 General Method of Solution

18.2 Illustrative Examples
18.3 Special Types of First Order Equations
18.4 Summary
18.5 Keywords
18.6 Review Questions
18.7 Further Readings

Objectives

After studying this unit, you should be able to see that:
 Charpit s method is used to find the general integral of the partial differential equation.
 This method introduces a second partial differential equation of the first order that contains
an arbitrary constant.
 With the help of this second equation and the original equation the partial derivatives
z z
p and , q can be found.
x y
 After finding these p and q, the solution can be found involving two arbitrary constants.

Introduction

With the help of the second equation and the original equation Charpit s subsidiary equations
are setup. Only those equations are to be solved that involve p or q.
Charpit s method helps in finding the general solution of the partial differential equations with
two arbitrary constants.

18.1 General Method of Solution

After discussing Lagrange s method and some special methods of solving partial differential
equation we now turn to an other general method due to Charpit in dealing with non-linear
partial differential equations involving two independent variables x and y. Here again we
z z
denote p and q . Let the given equation be of the first order only. So the equation to
x y
be sold will be of the form
F (x, y, z, p, q) = 0 ... (1)

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