# Plotting Vector Field in Mathematica

1. Oct 9, 2007

### robbondo

1. The problem statement, all variables and given/known data
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

2. Relevant equations

3. 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?

2. Oct 10, 2007

### EnumaElish

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.