Treat h as a constant. For what values of h (if any) does the following equation have equilibria? Use a graphical argument to show which of the equilibria (if any) are stable. dy -y³ - 6y-h =y dx HO Which of the equilibria, if any, are stable? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. There is one stable equilibrium when and there are no stable equilibria or other values of h. (Type your answer in inequality notation.) ◇ B. There are two stable equilibria when and there are no stable equilibria for other values of h. (Type your answer in inequality notation.)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Treat h as a constant. For what values of h (if any) does
the following equation have equilibria? Use a graphical
argument to show which of the equilibria (if any) are
stable.
dy
-y³ - 6y-h
=y
dx
HO
Which of the equilibria, if any, are stable? Select the
correct choice below and, if necessary, fill in the answer
box to complete your choice.
A. There is one stable equilibrium when
and
there are no stable equilibria or other values of h.
(Type your answer in inequality notation.)
◇ B. There are two stable equilibria when
and
there are no stable equilibria for other values of h.
(Type your answer in inequality notation.)
Transcribed Image Text:Treat h as a constant. For what values of h (if any) does the following equation have equilibria? Use a graphical argument to show which of the equilibria (if any) are stable. dy -y³ - 6y-h =y dx HO Which of the equilibria, if any, are stable? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. There is one stable equilibrium when and there are no stable equilibria or other values of h. (Type your answer in inequality notation.) ◇ B. There are two stable equilibria when and there are no stable equilibria for other values of h. (Type your answer in inequality notation.)
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