What is a Homogeneous Differential Equation?
All the equations of the following form are Homogenous Differential Equations.
dy/dx = f(x, y)/g(x, y)
where,
f(x, y) and g(x, y) are homogeneous functions of the degree n.
In simple words, a differential equation in which all the functions are of the same degree is called a homogeneous differential equation. For example, dy/dx = (x2 – y2)/xy is a homogeneous differential equation.
Examples of Homogeneous Differential Equations
Some more examples of the homogenous differential equation are,
- dy/dx = (2x + 3y)/(7x – y)
- dy/dx = 3x(x – y)/2y2
- dy/dx = (2x3 + 2xy2)/(y3 + 3yx2)
- dy/dx = (11x2 + xy)/2y2
In the above example, the degree of each term in the function is constant and hence, they are differential equations.
Homogeneous Differential Equations
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. 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.
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