Diferrential Equation question

Thread starter jofree87
Start date Jan 25, 2010

In summary, a differential equation is a mathematical equation that describes the relationship between a function and its derivatives. They are important because they are used to model and predict the behavior of complex systems, and have applications in fields such as physics, engineering, and economics. Solving a differential equation depends on the specific type, and common methods include separation of variables and substitution. Differential equations are used in everyday life to model natural phenomena and solve real-world problems in fields such as weather prediction, stock market analysis, and medical research.

Jan 25, 2010

jofree87

Show that y= 1/(x² - c) is a one parameter family of solutions of the differential equation dy/dx + 2xy² = 0

This might sound like a stupid question, but am I just suppose to find the derivative of y and plug that into the differential equation and see if the solution is zero? Is that what they mean by "show"?

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Jan 25, 2010

Dick

Science Advisor

Homework Helper

I think that's exactly what they mean.

1. What is a differential equation?

A differential equation is a mathematical equation that describes the relationship between a function and its derivatives. It is used to model various physical phenomena and is widely used in fields such as physics, engineering, and economics.

2. Why are differential equations important?

Differential equations are important because they provide a powerful tool for understanding and predicting the behavior of complex systems. They are also used to solve many real-world problems, such as predicting the motion of objects, analyzing electric circuits, and modeling population growth.

3. How do you solve a differential equation?

There is no one-size-fits-all method for solving differential equations, as the approach depends on the specific type of equation. However, some common techniques include separation of variables, substitution, and using integrating factors.

4. What are the applications of differential equations?

Differential equations have a wide range of applications in various fields, such as physics, engineering, economics, biology, and chemistry. They are used to model and analyze systems that involve rates of change, such as motion, growth, decay, and diffusion.

5. Are differential equations used in everyday life?

Yes, differential equations are used in everyday life to model and understand various natural phenomena. For example, they are used to predict the weather, analyze stock market trends, and design electrical circuits. They are also used in medical research to model the spread of diseases and in economics to study consumer behavior.