Classification of differential equation

In summary, the classification of a differential equation is based on its terms and helps determine the appropriate methods for solving it. Differential equations are classified based on their order, linearity, and degree. There are two types of differential equations: ordinary and partial. ODEs are classified as first-order or higher-order and can be linear or nonlinear. Common methods for solving differential equations include separation of variables, substitution, and various numerical and analytical methods.
  • #1
volican
41
0
Hi,

I have an equation that takes the form: ax''-by' + c = 0 where x'' is second order with respect to time and y' is first order with respect to time. Would this be classed as a partial differential equation?

Thanks very much for your help :)
 
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  • #2
Partial differential equations deal with functions of more than one variable. It looks as if yours is a single independent variable only equation.
 

1. What is the classification of differential equation?

The classification of a differential equation refers to the type of equation it is, based on the structure and properties of its terms. This classification helps determine the appropriate methods for solving the equation.

2. How are differential equations classified?

Differential equations are classified based on the order, linearity, and degree of the equation. The order refers to the highest derivative present in the equation, linearity refers to whether the equation is linear or nonlinear, and degree refers to the highest power of the derivative present in the equation.

3. What are the types of differential equations?

The types of differential equations include ordinary differential equations (ODEs) and partial differential equations (PDEs). ODEs involve only one independent variable, while PDEs involve multiple independent variables.

4. How are ODEs classified?

ODEs are classified as either first-order or higher-order, depending on the highest derivative present in the equation. They are further classified as linear or nonlinear based on the relationship between the dependent variable and its derivatives.

5. What are some common methods for solving differential equations?

Some common methods for solving differential equations include separation of variables, substitution, and the method of undetermined coefficients. Other methods include Laplace transforms, power series, and numerical methods such as Euler's method and the Runge-Kutta method.

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