For option A Y = 0, 3, 5; while for B Y(o) E [0,5]. The limit of Sdⁿ is Limited. See the definition of equilibrium solution below.
What is Equilibrium Solution?
A solution to a DE whose derivative is zero everywhere is an equilibrium solution.
A horizontal line represents an equilibrium solution on a graph.
You can identify equilibrium solutions given a slope field by locating every place where a horizontal line fits into the slope field.
What is the justification for the above answer?
Note that The Equilibrium solutions when Y' = 0 is:
⇒ y (y-3) (y-5) = =
⇒ Y = 0, y = 3, y = 5
hence,
Y = 0,3,5
For section B:
Given the stated Direction field, we know that:
If y(0) ∈ (0,5), then [tex]\lim_{x \to \infty }[/tex] y is 3
If y(0) ∈ (3,5), then [tex]\lim_{x \to \infty }[/tex] y is 3
With regards to values existing beyond the intervals, the result is divergent.
Therefore,
For y (0) ∈ [0,5], limit of Sdⁿ is Limited.
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Full Question:
Consider The Direction Field Below For A Differential Equation Y'=Y(Y?3)(Y?5).
Use The Graph And Equation To Answer The Following Questions.
1) Find The Equilibrium Solutions For The Differential Equation. Answer (Separate By Commas): Y=
2. If The Initial Condition Is Y(0)=C, For What Values Of C Is Limit??Y(T) Finite? Answer (As An Interval): See attached for related Image.
