Page 303 - DMTH504_DIFFERENTIAL_AND_INTEGRAL_EQUATION

Differential and Integral Equation Sachin Kaushal, Lovely Professional University

Notes Unit 20: Higher Order Equations with Constant
Coefficients and Monge’s Method

CONTENTS
Objectives

Introduction
20.1 Linear Partial differential equations of order n with constant coefficients;
complementary functions
20.2 Case when the auxiliary equation has equal roots

20.3 The Particular Integral (P.I.)
20.4 Shorter Method for Finding Particular Integral

20.5 General Method for Finding Particular Integral (P.I.)
20.6 The Non-homogeneous Equation with Constant Coefficients

20.7 Equation Reducible to Homogeneous Linear Form
20.8 Monge’s Method
2
20.9 Monge’s Method of integrating Rr + Ss + Tt + U (rt s ) = V
20.10 Summary

20.11 Keywords
20.12 Review Questions

20.13 Further Readings

Objectives

After studying this unit, you should be able to:
 Set up partial differential equations having higher order than that of first order.

 Know that various methods are employed depending upon the structure of the partial
differential equation.
 See that each section is followed by a set of self assessment problems related to that
section. By solving these problems the method can be understood.

Introduction

This section of the unit needs more practise for solving the various types of partial differential
equations.

The problems are classified according to the method used in solving them. It is therefore essential
to understand the method and its subsequent steps of solving the problem.

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