Various DE problems and related stuff - help

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SUMMARY

The discussion centers on challenges faced in a Differential Equations (DE) class, specifically regarding the construction of direction fields. The user expresses confusion about how to handle constants in the logistics equation, particularly the values of r, a, and b. It is established that while these constants can be set to arbitrary values for initial exploration, caution is advised against setting any constant to zero, as it may eliminate critical components of the equation.

PREREQUISITES
  • Understanding of Differential Equations and their applications
  • Familiarity with direction fields and their significance in DE analysis
  • Basic knowledge of logistics equations and their parameters
  • Ability to manipulate and analyze mathematical constants in equations
NEXT STEPS
  • Research how to construct direction fields for Differential Equations
  • Learn about the implications of setting constants in logistics equations
  • Explore the role of parameters in modeling real-world scenarios using DE
  • Study examples of direction fields with varying constant values to understand their effects
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Students in Differential Equations courses, educators teaching DE concepts, and anyone seeking to understand the practical applications of logistics equations in mathematical modeling.

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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.
 

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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.
 

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