What's your favourite type of differential equation

Thread starter J77
Start date Mar 27, 2006
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Differential Differential equation Type

In summary, a differential equation is a mathematical equation used to describe the relationship between an unknown function and its derivatives. There are different types of differential equations, including ordinary, partial, and stochastic, which can be classified based on their order and linearity. Differential equations play a crucial role in science, particularly in physics and engineering, as they are used to model and solve real-world problems. There is no favourite type of differential equation for scientists, as each type has its own unique properties and applications. Solving a differential equation involves finding a function that satisfies the equation, which can be done using various methods such as separation of variables, substitution, or special techniques like Laplace transforms or power series. Numerical solutions using computer software are also possible

Mar 27, 2006

J77

Just a small list, mark up any others I have neglected...

edit: already see, I should've put in PDEs with delay...

Last edited: Mar 27, 2006

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Mar 27, 2006

mathwonk

Science Advisor

Homework Helper

my fave is the several variable complex heat equation, to which riemann's theta function is a fundamental solution.

Mar 27, 2006

Clausius2

Science Advisor

Gold Member

I've started to enjoy those equations with a small [tex]\epsilon<<1[/tex] just in front of the highest order term...

What is a differential equation?

A differential equation is a mathematical equation that involves an unknown function and its derivatives. It describes the relationship between the function and its derivatives, and is commonly used to model physical phenomena in science and engineering.

What are the different types of differential equations?

There are several types of differential equations, including ordinary differential equations, partial differential equations, and stochastic differential equations. Additionally, differential equations can be classified based on their order (the highest derivative present) and linearity (whether the function and its derivatives are raised to a power or not).

What is the role of differential equations in science?

Differential equations play a crucial role in science, particularly in physics and engineering. They are used to model and solve real-world problems, such as predicting the motion of objects, analyzing electrical circuits, and understanding the spread of diseases.

What is your favourite type of differential equation?

As a scientist, I do not have a favourite type of differential equation. Each type has its own unique properties and applications, and they are all important in different areas of science and engineering.

How do you solve a differential equation?

Solving a differential equation involves finding a function that satisfies the equation. There are various methods for solving different types of differential equations, including separation of variables, substitution, and using special techniques such as Laplace transforms or power series. In some cases, differential equations can also be solved numerically using computer software.