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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 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 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.
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.
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 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
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 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 is monge's Method?
Monge's method, also known as the method of characteristics, is a mathematical technique used to solve certain types of partial differential equations. It involves transforming a partial differential equation into a system of ordinary differential equations by introducing characteristic curves. By solving these ordinary differential equations, one can find a solution to the original partial differential equation.
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.
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 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.
