Plotting Vector Field in Mathematica

So, it seems like you are trying to plot a vector field for the differential equation y'= ay-by^2-q, where a and b are positive constants, and q is an arbitrary constant. You also mention that y(0) = y_0 is the initial condition. After trying to plot this using vectorfieldplot, you encounter errors. You wonder if you need to manipulate the equation before attempting to plot it.
  • #1
robbondo
90
0

Homework Statement


y'=ay-by^2-q, where a, b are positive constants, and q is an arbitrary constant. In the following, y denotes a solution of this equation that satisfies the initial condition y(0) = y_0.
a. Choose a and b positive and q < a^2/4b. By plotting direction fields and solutions of A on suitable rectangular grids

R = {0<t<T,c<y<d}
in the ty plane , discover that there are numbers y1 and y2 with y1<y2 such that if
y_0>y1 the the lim as t approaches infiniti of y(t) = y_2, while if y_0<y1 then y(t) = negative infiniti for some value of t


Homework Equations





The Attempt at a Solution



Well I tried plotting using vectorfieldplot, it works fine for the equation w/o the constants a and b. But when i plug those in, it's error city. Do I need to manipulate this equation prior to attempting to plot it?
 
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  • #2
Mathematica evaluates the function being plotted and it cannot do that if it doesn't know what a and b stand for. You need to input specific values for these parameters.
 
  • #3


It is possible that the error is due to the values you have chosen for a, b, and q. Make sure they are positive and that q is less than a^2/4b. Also, you may need to adjust the range of your grid to better capture the behavior of the solutions. Try experimenting with different values for t and y to see if you can get a better plot. It is also possible that the equation needs to be manipulated before plotting, so you may want to double check your work and see if there are any simplifications or substitutions that can be made to make it easier to plot.
 

1. How do I plot a vector field in Mathematica?

To plot a vector field in Mathematica, you can use the VectorPlot function. This function takes in the vector field as an input and generates a plot with arrows representing the direction and magnitude of the vectors.

2. Can I customize the appearance of my vector field plot?

Yes, you can customize the appearance of your vector field plot by using optional parameters in the VectorPlot function. These parameters allow you to change the color, size, and style of the arrows, as well as the overall layout of the plot.

3. How do I add labels and legends to my vector field plot?

To add labels and legends to your vector field plot, you can use the PlotLabel and PlotLegends options in the VectorPlot function. These options allow you to add a title and a legend to your plot, making it more informative.

4. Can I plot multiple vector fields in one plot?

Yes, you can plot multiple vector fields in one plot by using the VectorPlot function with multiple inputs. You can also use the Show function to combine multiple plots into one.

5. How do I export my vector field plot as an image or a vector graphics file?

To export your vector field plot as an image, you can use the Export function and specify the desired file format. If you want to export your plot as a vector graphics file, you can use the EpsGraphics or PDF options in the Export function.

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