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afcwestwarrior
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Homework Statement
For what values of K does the function y=cos k t satisft the differential equation 4y"=-25y?
Do I have to find the derivative of y twice or what do i do
A differential equation is a mathematical equation that describes the relationship between a function and its derivatives. It is used to model physical phenomena and is commonly used in science and engineering fields.
An ordinary differential equation involves only one independent variable, while a partial differential equation involves multiple independent variables. Ordinary differential equations are used to model situations that are changing over time, while partial differential equations are used to model situations that are changing over multiple dimensions.
Differential equations can be solved analytically or numerically. Analytical solutions involve finding an expression for the function that satisfies the equation, while numerical solutions involve using algorithms to approximate the solution.
Differential equations are used to model a wide range of phenomena in the natural and physical sciences, engineering, and economics. Some common applications include modeling population growth, predicting weather patterns, and solving electrical circuit problems.
While differential equations are a powerful tool for modeling and understanding complex systems, they do have limitations. Some equations may not have analytic solutions, making numerical approximations necessary. Additionally, they may not accurately represent systems with chaotic behavior or systems with rapidly changing parameters.