Non-Homogeneous Differential Equation
Any differential equation which is not Homogenous is called a Non-Homogenous Differential Equation. The general form of the linear non-homogeneous differential equation of second order is,
y”+a(t)y’+b(t)y = c(t)
Where,
- y” represents the second-degree differentiation of y, and
- c(t) is a non-zero function.
The above non-homogenous differential equation can be converted to a homogeneous differential equation and the related DE is,
y”+a(t)y’+b(t)y = 0
This equation is also called the complementary equation to the given non-homogeneous differential equation.
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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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