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What is the application of the ordinary differential equation?

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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 the use of differential equation in computer science engineering?

There is no application of differential equation in computer science


Example of total partial and original differential equation?

An ordinary differential equation (ODE) has only derivatives of one variable.


What is nonlinear ordinary differential equation?

An ordinary differential equation is an equation relating the derivatives of a function to the function and the variable being differentiated against. For example, dy/dx=y+x would be an ordinary differential equation. This is as opposed to a partial differential equation which relates the partial derivatives of a function to the partial variables such as d²u/dx²=-d²u/dt². In a linear ordinary differential equation, the various derivatives never get multiplied together, but they can get multiplied by the variable. For example, d²y/dx²+x*dy/dx=x would be a linear ordinary differential equation. A nonlinear ordinary differential equation does not have this restriction and lets you chain as many derivatives together as you want. For example, d²y/dx² * dy/dx * y = x would be a perfectly valid example


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.


Application of differential equation in chemistry?

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


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.


How many types of auxiliary condition in ordinary differential equation?

it has two types


What is the global solution of an ordinary differential equation?

The global solution of an ordinary differential equation (ODE) is a solution of which there are no extensions; i.e. you can't add a solution to the global solution to make it more general, the global solution is as general as it gets.


In mathematics what does the abbreviation PDE stand for?

The abbreviation PDE stands for partial differential equation. This is different from an ordinary differential equation in that it contains multivariable functions rather than single variables.


Application of differential equation in temperature?

Newton's equation of cooling is a differential equation. If K is the temperature of a body at time t, then dK/dt = -r*(K - Kamb) where Kamb is the temperature of the surrounding, and r is a positive constant.


What are the Uses of Cauchy Euler equation?

One thing about math is that sometimes the challenge of solving a difficult problem is more rewarding than even it's application to the "real" world. And the applications lead to other applications and new problems come up with other interesting solutions and on and on... But... The Cauchy-Euler equation comes up a lot when you try to solve differential equations (the Cauchy-Euler equation is an ordinary differential equation, but more complex partial differential equations can be decomposed to ordinary differential equations); differential equations are used extensively by engineers and scientists to describe, predict, and manipulate real-world scenarios and problems. Specifically, the Cauchy-Euler equation comes up when the solution to the problem is of the form of a power - that is the variable raised to a real power. Specific cases involving equilibrium phenomena - like heat energy through a bar or electromagnetics often rely on partial differential equations (Laplace's Equation, or the Helmholtz equation, for example), and there are cases of these which can be separated into the Cauchy-Euler equation.


Applications of ordinary differential equations in engineering field?

Applications of ordinary differential equations are commonly used in the engineering field. The equation is used to find the relationship between the various parts of a bridge, as seen in the Euler-Bernoulli Beam Theory.


What is the local solution of an ordinary differential equation?

The local solution of an ordinary differential equation (ODE) is the solution you get at a specific point of the function involved in the differential equation. One can Taylor expand the function at this point, turning non-linear ODEs into linear ones, if needed, to find the behavior of the solution around that one specific point. Of course, a local solution tells you very little about the ODE's global solution, but sometimes you don't want to know that anyways.


What is an ordinary differential equation?

It is one in which there is only one independent variable, ie there are no partial derivatives. For example, (dy/dx) + 2y = cosx + x


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.


What is differential equation in mathematics?

An equation in terms of functions and its nth-order derivatives. For example, dy/dx = x^2 + y is a differential equation.


What has the author Witold Hurewicz written?

Witold Hurewicz has written: 'Lectures on Ordinary Differential Equations' 'Ordinary differential equations in the real domain with emphasis on geometric methods' -- subject(s): Differential equations


What is differential equations as it relates to algebra?

It is an equation in which one of the terms is the instantaneous rate of change in one variable, with respect to another (ordinary differential equation). Higher order differential equations could contain rates of change in the rates of change (for example, acceleration is the rate of change in the rate of change of displacement with respect to time). There are also partial differential equations in which the rates of change are given in terms of two, or more, variables.


What is an equation that contains a variable?

It is an equation. It could be an algebraic equation, or a trigonometric equation, a differential equation or whatever, but it is still an equation.


Who invented the ordinary differential equations?

Olusola Akinyele


Who is father of differential equation?

leibniz


Application of differential pair while routing?

i want exact meaning of differential pair(or)definition & where its used ie.,(application) & advantage &disadvantage.


What is the general solution of a differential equation?

It is the solution of a differential equation without there being any restrictions on the variables (No boundary conditions are given). Presence of arbitrary constants indicates a general solution, the number of arbitrary constants depending on the order of the differential equation.


Heat equation partial differential?

Yes, it is.


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