Differential equation question

Thread starter nhrock3
Start date Oct 20, 2010
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Differential Differential equation

In summary, a differential equation is a mathematical equation that describes the relationship between a function and its derivatives. An ordinary differential equation involves one independent variable, while a partial differential equation involves multiple independent variables. These equations are used in a variety of real-world applications, from predicting population growth to modeling electrical circuits. There are several methods for solving differential equations, including numerical methods. However, some real-world problems, such as chaotic systems, cannot be solved using differential equations and may require other mathematical tools.

Oct 20, 2010

nhrock3

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Oct 20, 2010

Char. Limit

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What have you tried so far?

Also, don't just post a pic. Most members wouldn't click it. Post the problem here, and show us what you've tried to solve it.

1. What is a differential equation?

A differential equation is a mathematical equation that describes the relationship between a function and its derivatives. It involves variables and their rates of change, and is commonly used to model complex systems in physics, engineering, and other fields.

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

An ordinary differential equation involves only one independent variable, while a partial differential equation involves more than one independent variable. This means that the derivatives in a partial differential equation are taken with respect to multiple variables, making it more complex to solve.

3. How are differential equations used in real-world applications?

Differential equations are used in a wide range of real-world applications, such as predicting population growth, modeling the spread of diseases, and analyzing the behavior of electrical circuits. They are also commonly used in physics to describe the motion of objects and in economics to model economic systems.

4. What methods are used to solve differential equations?

There are several methods used to solve differential equations, including separation of variables, substitution, and using integrating factors. Numerical methods, such as Euler's method and Runge-Kutta methods, are also commonly used to approximate solutions to more complex differential equations.

5. Are there any real-world problems that cannot be solved using differential equations?

While differential equations are a powerful tool for modeling real-world systems, there are some problems that cannot be solved using them. For example, chaotic systems and systems with random variables may not have a deterministic solution using differential equations. In these cases, other mathematical tools, such as stochastic processes, may be needed to model the system.