Question

The equation Pp + Qq = R is known as ​

Answer 1

Answer:

Lagrange's Linear Equation

A partial differential equation of the form Pp+Qq=R where P, Q, R are functions of x, y, z (which is or first order and linear in p and q) is known as Lagrange's Linear Equation.

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Answer 2

The given equation is known as Lagrange's Equation.

Lagrange's Equation:

a) A particular Quasi-linear partial differential equation of order one is of the form Pp + Qq = R, where P, Q, and R are functions of x, y, z. This type of partial differential equation is called the Lagrange equation.

b) For Example,  abp + cdq = dx is a Lagrange equation.

Theorem:

. The general solution of Lagrange equation Pp + Qq = R is where Q is an arbitrary function and u(a, b, c) = x1 and the  v (a, b, c) = x2 are two independent solutions of (dx)/P = (dy)/Q = (dz)/R.

Pp + Qq = R

Ф(u, v) = 0

u(a, b, c) = x1 and the v(a, b, c) = x2

(dx)/P = (dy)/Q = (dz)/R