A DE deduced from the direction field

In summary, a DE, or differential equation, is a mathematical equation used to describe the change of one or more variables over time or in relation to each other. A direction field is a graphical representation of a DE that helps visualize its behavior and aid in finding solutions. A DE can be deduced from a direction field by analyzing the direction of the line segments at different points on the plane. This information can then be used to determine the behavior and solutions of the DE, which is useful in scientific research for modeling and analyzing natural phenomena.
  • #1
ehabmozart
213
0

Homework Statement



Which of the following di erential equations corresponds to the direction eld
shown below?

1) y'=x+y
2) y'=xy-1
3) y'=1-xy
4) y'-xy
5) y'=x-y


Homework Equations





The Attempt at a Solution



I have no idea how can this be done. I mean I used to deduce the DE from the direction field only when the equilibrium solution was HORIZONTAL.. Now, I am confused! Anyone who would help, I would appreciate it.
 

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  • #2
For what (x,y) is y'=0 in the picture?
 

FAQ: A DE deduced from the direction field

1. What is a DE?

A DE, or differential equation, is a mathematical equation that describes how one or more variables change over time or in relation to each other. It involves the use of derivatives and is commonly used in the field of mathematics and science to model various phenomena.

2. What is a direction field?

A direction field is a graphical representation of a DE, where small line segments are drawn at various points on a coordinate plane to show the direction in which the solution curves would move at those points. It helps visualize the behavior of the DE and can aid in finding solutions.

3. How is a DE deduced from a direction field?

A DE can be deduced from a direction field by analyzing the direction of the line segments at different points on the plane. The slope of the line segments can be used to determine the derivative of the function at that point, which can then be used to write the DE in terms of the independent and dependent variables.

4. What information can be gathered from a DE deduced from a direction field?

A DE deduced from a direction field can provide information about the behavior and solutions of the DE. It can help determine if the DE has a unique solution or multiple solutions, if the solutions are stable or unstable, and how the solutions change over time.

5. How is a DE deduced from a direction field used in scientific research?

A DE deduced from a direction field is commonly used in scientific research to model and analyze various natural phenomena, such as population growth, chemical reactions, and physical processes. By understanding the behavior of the DE, scientists can make predictions and gain insights into real-world systems.

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