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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
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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 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.
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.
True or false In a nonlinear equation each variable must only have one solution?
In a nonlinear equation, each variable must only have one solution.
What has the author R Grimshaw written?
R. Grimshaw has written: 'Nonlinear ordinary differential equations' -- subject(s): Nonlinear Differential equations
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 has the author P L Sachdev written?
P. L. Sachdev has written: 'A compendium on nonlinear ordinary differential equations' -- subject(s): Differential equations 'Large time asymptotics for solutions of nonlinear partial differential equations' -- subject(s): Nonlinear Differential equations, Asymptotic theory, Nichtlineare partielle Differentialgleichung
Example of total partial and original differential equation?
An ordinary differential equation (ODE) has only derivatives of one variable.
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 has the author D J MURRAY written?
J. D. Murray has written: 'Lectures on nonlinear-differential-equation models in biology' -- subject(s): Biology, Differential equations, Nonlinear, Mathematical models, Nonlinear Differential equations
How many types of auxiliary condition in ordinary differential equation?
it has two types
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 has the author Elemer E Rosinger written?
Elemer E. Rosinger has written: 'Generalized solutions of nonlinear partial differential equations' -- subject(s): Differential equations, Nonlinear, Differential equations, Partial, Nonlinear Differential equations, Numerical solutions, Partial Differential equations 'Distributions and nonlinear partial differential equations' -- subject(s): Differential equations, Partial, Partial Differential equations, Theory of distributions (Functional analysis)
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.
What has the author Rudolph Ernest Langer written?
Rudolph Ernest Langer has written: 'On the asymptotic solutions of ordinary linear differential equations about a turning point' -- subject(s): Differential equations, Linear, Linear Differential equations 'Nonlinear problems' -- subject(s): Nonlinear theories, Congresses 'A first course in ordinary differential equations' -- subject(s): Differential equations 'Partial differential equations and continuum mechanics' -- subject(s): Congresses, Differential equations, Partial, Mathematical physics, Mechanics, Partial Differential equations 'Boundary problems in differential equations' -- subject(s): Boundary value problems, Congresses
What has the author Enzo Mitidieri written?
Enzo Mitidieri has written: 'Apriori estimates and blow-up of solutions to nonlinear partial differential equations and inequalities' -- subject(s): Differential equations, Nonlinear, Differential equations, Partial, Inequalities (Mathematics), Nonlinear Differential equations, Partial Differential equations
