# Differential Equations-Finding Constants

1. Aug 7, 2013

### Bashyboy

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:

• ###### DiffEq 331HW1.pdf
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Last edited: Aug 7, 2013
2. Aug 7, 2013

### voko

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.