Vector Plots-Direction Field ODE

In summary, the Mathematica output accurately represents the given ODE and shows the relationship between the derivatives of y and x.
  • #1
pat666
709
0

Homework Statement



More mathematica - I just want to know if what I have gotten mathematica to do is representative of my ODE.

Homework Equations


The Attempt at a Solution


The Question was:
[tex]x^3y'+xy=x[/tex] which I put in the form
[tex]y'=(xy-x)/(-x^3) [/tex]
I at very least have a pretty picture to hand in. Could someone tell me if it is representative of this ode or what I am looking for to tell if it is.
The pic is attached.

Thanks
 

Attachments

  • Untitled-1.png
    Untitled-1.png
    13.2 KB · Views: 485
Physics news on Phys.org
  • #2
!Yes, it looks like your Mathematica output is representative of the given ODE. You can see that the graph shows the relationship between the derivatives of y and x, which is what the ODE specifies. This is a good representation of your ODE.
 

FAQ: Vector Plots-Direction Field ODE

1. What is a vector plot or direction field in ODEs?

A vector plot or direction field is a graphical representation of the slope or direction of a system of ordinary differential equations (ODEs) at different points in the solution space. It is created by plotting arrows at various points in the solution space, with the direction and magnitude of each arrow representing the slope or direction of the ODEs at that point.

2. Why are vector plots or direction fields useful in studying ODEs?

Vector plots or direction fields provide a visual representation of the behavior of a system of ODEs. It allows us to see how the solution to the ODEs changes as the initial conditions or parameters are varied. This can help us better understand the dynamics of the system and make predictions about its behavior.

3. How are vector plots or direction fields created?

Vector plots or direction fields are created using software or programming languages that can solve systems of ODEs, such as MATLAB or Python. The solution to the ODEs is calculated at various points in the solution space, and arrows are plotted at these points based on the calculated slope or direction. The resulting plot is the vector plot or direction field.

4. What information can be obtained from a vector plot or direction field?

A vector plot or direction field can provide information about the behavior of a system of ODEs, such as the stability of equilibrium points, the presence of limit cycles, and the direction of flow of the solution. It can also help in identifying critical points and making predictions about the long-term behavior of the system.

5. Are there any limitations to using vector plots or direction fields in studying ODEs?

Vector plots or direction fields can only provide a qualitative understanding of the behavior of a system of ODEs. They do not provide exact solutions or numerical values, and the accuracy of the plot depends on the precision of the software or programming language used. Additionally, vector plots or direction fields may become complex and difficult to interpret for systems with more than two variables.

Similar threads

Finding the flow of a vector field
Replies
5
Views
2K
Mathematica - How to Graph Direction Fields of ODEs?
Replies
9
Views
487
Show that ODE is homogeneous, but I don't think it is
Replies
2
Views
1K
Existence and Uniqueness For ODE
Replies
6
Views
1K
Solving ODEs with Laplace. Stuck at Partial Fraction Expansi
Replies
3
Views
2K
Question on Two Differentiation Techniques
Replies
25
Views
1K
Plotting the approximation of the Dirac delta function
Replies
3
Views
678
Finding the homogenous solution of Var.Coeff. 2nd Order ODE
Replies
3
Views
1K
How Do Matrix ODEs Relate to Determinants and Traces?
Replies
3
Views
1K
Exact ODE and Finding Integrating Factors
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top