Homogeneous differential equation questions and answers pdf

Homogeneous Differential Equations are differential equations with homogenous functions. They are equations containing a differentiation operator, a function, and a set of variables.

The general form of the homogeneous differential equation is f(x, y).dy + g(x, y).dx = 0, where f(x, y) and h(x, y) is a homogenous function. Homogenous functions are defined as functions in which the total power of all the terms of the function is constant.

First order homogeneous differential equation

Before continuing with Homogeneous Differential Equations we should learn Homogeneous Functions first. In this article, we will learn about, Homongenous Functions, Homogeneous Differential Equations, their solutions, and others in detail.

What is a Homogeneous Function?

A function f(x, y) in x and y is said to be a homogeneous function if the degree of each term in the function is constant (say p).

For example, f(x, y) = (x² + y² – xy) is a homogeneous function of degree 2 where p = 2. Similarly, g(x, y) = (x³ – 3xy² + 3x²y + y³) is a homogeneous function of degree 3 where p = 3. 

when a differential equation is called homogeneous

when is an equation homogeneous