Plotting Direction Fields for Differential Equations: A Mathematica Tutorial

In summary, the conversation discusses how to plot the direction field of a given equation and the issue of getting error messages due to incorrect values of y. It is suggested to use a certain range for y values to avoid the error. The concept of a direction field is also mentioned and a resource is provided for further understanding.
  • #1
DivGradCurl
372
0
Does anybody know how to plot the direction field of [tex]y^{\prime} = 5 - 3\sqrt{y}[/tex]?

I get error messages because the independent variable isn't there. I've attached a mathematica notebook that shows it.

Any help is highly appreciated.
 

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  • DirectionField.zip
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  • #2
thiago_j said:
Does anybody know how to plot the direction field of [tex]y^{\prime} = 5 - 3\sqrt{y}[/tex]?

I get error messages because the independent variable isn't there. I've attached a mathematica notebook that shows it.

Any help is highly appreciated.

Your Y values cannot be less than 0 since it has a y^.5, that's what is messing you up...stick to {y, 0, 10} and you will be fine...
 
  • #3
You're definitely right. It has nothing to do with the independent variable, and I should have paid attention to the values of y. It works now! Thank you very much.
 
  • #4
What's a direction field?
 
  • #6
Thanks, thiago_j.
 

1. What is a direction field/slope field?

A direction field, also known as a slope field, is a graphical representation of the slope at different points on a two-dimensional plane. It is created by drawing short line segments with slopes that correspond to the slopes of the tangent lines at each point on the plane.

2. What is the purpose of a direction field/slope field?

The purpose of a direction field/slope field is to visually represent the behavior of a differential equation. By looking at the direction and density of the slope lines, one can get an idea of the overall solution to the equation and how it changes at different points on the plane.

3. How is a direction field/slope field created?

A direction field/slope field is created by plotting a grid of points on a two-dimensional plane. At each point, the slope of the tangent line is calculated using the given differential equation. A short line segment with the calculated slope is then drawn at each point, creating a field of slope lines.

4. What information can be obtained from a direction field/slope field?

A direction field/slope field can provide information about the direction and magnitude of the slope at different points on the plane. This information can be used to estimate the behavior of the solution to the given differential equation and to identify critical points, such as maxima and minima.

5. How is a direction field/slope field useful in solving differential equations?

A direction field/slope field provides a visual representation of the behavior of a differential equation, which can help in understanding the solution to the equation. It can also provide insight into the existence and stability of solutions, as well as the behavior of the solution at different points on the plane.

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