Transforms And Partial Differential Equations: UNIT I: Partial Differential Equations

Lagrange's Linera Equation

Home | All Subjects | CIVIL Department | Transforms and Partial Differential Equations
Next >>

The equation of the form Pp+ Qq= R is known as Lagrange's equation when P, Q & R are functions of x, y and z.

LAGRANGE'S LINEAR EQUATION

The equation of the form Pp+ Qq= R is known as Lagrange's equation when P, Q & R are functions of x, y and z.


Working Rule

First step: Write down the subsidiary equations


Second step: Solve the above subsidiary equations.

Let the two solutions be u=a and v=b

Third step: Then f(u, v) = 0 or u = (v) is the required

solution of P p + Qq = R

Generally, the subsidiary equation can be solved in two ways.

1. Method of Grouping

2. Method of Multipliers

 

1. Method of Grouping

In the subsidiary equation ppppppppppp if the variables can be separated in any pair of equations, then we get a solution of the form u (x, y) = = a and v (x, y) = b.

2. Method of Multipliers

Choose any three multipliers 1, m, n which may be constants or function of x, y, z we have


If it is possible to choose l, m, n such that IP + mQ+nR then ldx + mdy + ndz = 0

If ldx + mdy+ndz is an exact differential then on integration we  get a solution u = a.

The multipliers l, m, n are called lagrangian multipliers.

Transforms And Partial Differential Equations: UNIT I: Partial Differential Equations : Tag: : - Lagrange's Linera Equation

Home | All Subjects | CIVIL Department | UNIT: Transforms and Partial Differential Equations
Next >>

Related Topics


Partial Differential Equations - Introduction

Formation of partial differential equations by elimination of arbitrary Constants

Problems based on formation of p.d.e by elimination of arbitrary constants (a.c.) - Partial Differential Equations

Exercise [formation of P.D.E by elimination of arbitrary constants (a.c.)] - Partial Differential Equations

Formation of partial differential equations by elimination of arbitrary functions

Solved Example Problems based on formation of p.d.e by elimination of arbitrary functions - Partial Differential Equations

Exercise [formation of p.d.e by elimination of arbitrary functions] - Partial Differential Equations

Solved Example Problems based on Formation of p.d.e by elimination of arbitrary functions - Partial Differential Equations

Exercise [Form the p.d.e by eliminating the arbitrary functions] - Partial Differential Equations

Singular Integrals - Solution of Standard Types of First Order Partial Differential Equations - Partial Differential Equations

Exercise [partial differential equation]

Methods to solve the first order partial differential equation

Solved Example Problems based on First order Partial Differential Equations (p.d.e)

Exercise [First order Partial Differential Equations]

Solved Example Problems based on Type 2 Clairaut's form z = = px + qy + f (p, q) - Partial Differential Equations

Related Subjects


Transforms and Partial Differential Equations

Transforms and Partial Differential Equations

MA3351 3rd semester civil, Mechanical Dept | 2021 Regulation | 3rd Semester Mechanical Dept 2021 Regulation