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a linear first-order differential equation is homogenous if its right hand side is zero & A linear first-order differential equation is non-homogenous if its right hand side is non-zero.

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Why x-3 equals 0 is non homogeneous?

Because homogeneous equations normally refer to differential equations. The one in the question is not a differential equation.


What is the difference between an ordinary differential equation and a partial differential equation?

ordinary differential equation is obtained only one independent variable and partial differential equation is obtained more than one variable.


What is constant in differential equation?

In the context of differential equations, a constant typically refers to a fixed value that does not change with respect to the variables in the equation. Constants can appear as coefficients in the terms of the equation or as part of the solution to the equation, representing specific values that satisfy initial or boundary conditions. They play a crucial role in determining the behavior of the solutions to differential equations, particularly in homogeneous and non-homogeneous cases.


What is the difference between a first order and a second order differential equation?

A first order differential equation involves only the first derivative of the unknown function, while a second order differential equation involves the second derivative as well.


What is the difference between fuzzy differential equation and ordinary differential equation?

fuzzy differential equation (FDEs) taken account the information about the behavior of a dynamical system which is uncertainty in order to obtain a more realistic and flexible model. So, we have r as the fuzzy number in the equation whereas ordinary differential equations do not have the fuzzy number.


What is non trivial solution of non homogeneous equation?

A non-trivial solution of a non-homogeneous equation is a solution that is not the trivial solution, typically meaning it is not equal to zero. In the context of differential equations or linear algebra, a non-homogeneous equation includes a term that is not dependent on the solution itself (the inhomogeneous part). Non-trivial solutions provide meaningful insights into the behavior of the system described by the equation, often reflecting real-world phenomena or constraints.


What is Exact ordinary differential equation?

exact differential equation, is a type of differential equation that can be solved directly with out the use of any other special techniques in the subject. A first order differential equation is called exact differential equation ,if it is the result of a simple differentiation. A exact differential equation the general form P(x,y) y'+Q(x,y)=0Differential equation is a mathematical equation. These equation have some fractions and variables with its derivatives.


What is impulsive differential equation?

Differential equation is defined in the domain except at few points (may be consider the time domain ti ) may be (finite or countable) in the domain and a function or difference equation is defined at each ti in the domain. So, differential equation with the impulsive effects we call it as impulsive differential equation (IDE). The solutions of the differential equation is continuous in the domain. But the solutions of the IDE are piecewise continuous in the domain. This is due to the nature of impulsive system. Generally IDE have first order discontinuity. There are so many applications for IDE in practical life.


what is differential equation?

Differential equation is defined in the domain except at few points (may be consider the time domain ti ) may be (finite or countable) in the domain and a function or difference equation is defined at each ti in the domain. So, differential equation with the impulsive effects we call it as impulsive differential equation (IDE). The solutions of the differential equation is continuous in the domain. But the solutions of the IDE are piecewise continuous in the domain. This is due to the nature of impulsive system. Generally IDE have first order discontinuity. There are so many applications for IDE in practical life.


What is the differential pressure equation used to calculate the pressure difference between two points in a fluid system?

The differential pressure equation used to calculate the pressure difference between two points in a fluid system is P gh, where P is the pressure difference, is the density of the fluid, g is the acceleration due to gravity, and h is the height difference between the two points.


Application of differential equation in chemistry?

The rate at which a chemical process occurs is usually best described as a differential equation.


What is the Order of a differential equation?

The order of a differential equation is a highest order of derivative in a differential equation. For example, let us assume a differential expression like this. d2y/dx2 + (dy/dx)3 + 8 = 0 In this differential equation, we are seeing highest derivative (d2y/dx2) and also seeing the highest power i.e 3 but it is power of lower derivative dy/dx. According to the definition of differential equation, we should not consider highest power as order but should consider the highest derivative's power i.e 2 as order of the differential equation. Therefore, the order of the differential equation is second order.