Mathematica Plotting Vector Field in Mathematica

Click For Summary
The discussion focuses on plotting the vector field for the differential equation y' = ay - by^2 - q in Mathematica, where a and b are positive constants and q is an arbitrary constant. Users are encountering errors when trying to plot the equation with the constants included, as Mathematica requires specific values for a and b to evaluate the function correctly. It is suggested that the equation may need manipulation or simplification before plotting. The importance of defining parameters clearly in Mathematica is emphasized to avoid errors. Properly setting up the parameters is crucial for successfully visualizing the direction fields and solutions.
robbondo
Messages
90
Reaction score
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?
 
Physics news on Phys.org
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.
 

Similar threads

  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 1 ·
Replies
1
Views
4K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 3 ·
Replies
3
Views
7K
  • · Replies 3 ·
Replies
3
Views
2K
Replies
2
Views
1K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 10 ·
Replies
10
Views
2K