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Differential Equations-Finding Constants

  1. Aug 7, 2013 #1
    Differential Equations--Finding Constants

    1. The problem statement, all variables and given/known data
    I uploaded a pdf document, which contains the problem I am currently working on, namely, problem number 7


    2. Relevant equations



    3. The attempt at a solution
    I am having particular difficulty with this portion of the solution:

    "(ii) At y=3, the function ay+b changes from positive to negative
    --> ay+b has a negative slope --> a is negative"

    Why does "a" being negative follow from these facts? Also, why does a function change signs at y = 3?
     

    Attached Files:

    Last edited: Aug 7, 2013
  2. jcsd
  3. Aug 7, 2013 #2
    Two lines above, it was shown that ay + b > 0 when y < 3, and ay + b < 0 when y > 3. That literally means that it changes its sign at y = 3. And because it goes from positive to negative, it has to have a negative slope. Now this function is a simple straight line, so its slope = a, hence a must be negative.
     
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