What ordinary differential equation? Simple answer is needed

In summary, an ordinary differential equation (ODE) is a mathematical equation that relates one or more independent variables to a dependent variable and its derivatives. It differs from a partial differential equation (PDE) in that it only involves one independent variable and ordinary derivatives. ODEs are commonly used in various scientific fields to model and understand dynamic systems. An example of an ODE is Newton's Second Law equation. ODEs can be solved using various methods, including separation of variables, substitution, and numerical techniques.
  • #1
nalkapo
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What ordinary differential equation? Simple answer is needed!

Homework Statement


instead [delta] i will use 'd'.
in these two example, what kind of ordinary dif. eq. are implied by the methodd of separation of variables.
first one is;

du/dt=(d^2u)/(dx^2) - 5 du/dt

and other one is;

du/dt=2(d^4u/dx^4)

'd' is [delta] in these examples...
Thanks for now..

Homework Equations





The Attempt at a Solution


 
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  • #2


Well, what have you done? Since the problems refers to what you would get "by the methodd of separation of variables", what is the "method of separation of variables?
 

1. What is an ordinary differential equation?

An ordinary differential equation (ODE) is a type of mathematical equation that involves one or more independent variables, a dependent variable, and its derivatives. It describes the relationship between the variables and their rates of change.

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

The main difference is that an ordinary differential equation involves only one independent variable, while a partial differential equation involves multiple independent variables. ODEs also only have ordinary derivatives, while PDEs can have partial derivatives.

3. How are ordinary differential equations used in science?

ODEs are used to model and describe various physical and natural phenomena in the fields of physics, engineering, chemistry, biology, and other sciences. They help us understand the behavior and evolution of dynamic systems.

4. Can you give an example of an ordinary differential equation?

Sure, the classic example is the Newton's Second Law equation: F = ma, where F is the force, m is the mass, and a is the acceleration. This is a simple ODE that describes the relationship between force, mass, and acceleration.

5. How do you solve an ordinary differential equation?

There are various methods for solving ODEs, such as separation of variables, substitution, and integrating factors. The specific method used depends on the type and complexity of the equation. Sometimes, ODEs can also be solved numerically using computer software or approximated with numerical methods.

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