Drawing a direction field for the logistic equation with parameters

  • Thread starter WirelesssTouc
  • Start date
1 reply · 1K views · last reply
WirelesssTouc
Messages
1
Reaction score
0
My DE class has been 100% about solving equations giving an equation. But my teacher seems to think giving us a very wordy sheet of homework would be fun and I just seem to be very lost. Trying to go through this systematically starting with the first problem and I've no idea what to do.

I have to draw a direction field. I figured I could plug in various values of x and t to just get dx/dt, but I don't know what to do about the other variables, r, b, and a. Can I simply set r=1, a=1, and b=0, arbitrarily, since they would be random constants in the logistics equation in the first place? So lost.

Attached is all the assignment.
 
Attachments
  • Photo of a printed homework sheet with Exercises 6 to 10 on differential equations, including dx/dt = r x (at + b - x) with x < at + b and the Bernoulli equation part.
    lastscan.jpg
    46.2 KB · Views: 400
Yes, a, b, and r are constants. I would be a little careful about setting any constant to 0. That may remove important parts of the equation and so not be as general as you would like to.