Plotting Vector Field in Mathematica

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SUMMARY

The discussion focuses on plotting the vector field for the differential equation y' = ay - by² - q in Mathematica. Users must define positive constants a and b, and an arbitrary constant q, ensuring that q < a²/4b. The issue arises when attempting to plot the vector field using the function VectorFieldPlot, as Mathematica requires specific numerical values for a and b to evaluate the function correctly. The solution involves substituting concrete values for these parameters before plotting.

PREREQUISITES
  • Understanding of differential equations, specifically the form y' = f(y).
  • Familiarity with Mathematica software and its plotting functions.
  • Knowledge of parameter constraints in mathematical modeling.
  • Basic concepts of vector fields and direction fields.
NEXT STEPS
  • Learn how to use Mathematica's VectorFieldPlot with parameterized equations.
  • Explore the concept of stability in differential equations and how it relates to initial conditions.
  • Investigate the implications of parameter constraints in mathematical models.
  • Study the visualization techniques for direction fields in Mathematica.
USEFUL FOR

Students and educators in mathematics, particularly those studying differential equations, as well as Mathematica users looking to enhance their plotting skills and understand vector fields.

robbondo
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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.
 

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