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Kurret
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Im just curious, what is the highest order DE that has come up in physics, or other areas of applied mathematics? So far I have only encounter second orders in physics...
Differential equations are mathematical equations that involve an unknown function and its derivatives. They are used to describe the relationship between a quantity and its rate of change, making them important in physics and other sciences.
Differential equations are used in physics to model and predict the behavior of physical systems. They allow scientists to describe the relationship between a physical quantity and its rate of change, making them essential for understanding the laws of nature.
The order of a differential equation is the highest derivative present in the equation. For example, a first-order differential equation has a derivative of the first order, while a second-order differential equation has a derivative of the second order.
Exploring orders of differential equations is important because it allows scientists to understand the complexity of a system and determine the appropriate mathematical model to describe it. By analyzing the order of a differential equation, scientists can also predict the behavior of a system and make accurate calculations.
Differential equations have numerous real-world applications in physics and maths, such as modeling the movement of objects under the influence of gravity, predicting the spread of diseases, and understanding the behavior of electrical circuits. They are also used in engineering, economics, and other sciences to solve complex problems and make accurate predictions.