dy dt The following problem involves an equation of the form = f(y). Sketch the graph of f(y) versus y, determine the critical (equilibrium) points, and classify each one as asymptotically stable or unstable. Draw the phase line, and sketch several graphs of solutions in the ty-plane. dy = = y(64- y²), -∞

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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dy
dt
The following problem involves an equation of the form = f(y).
Sketch the graph of f(y) versus y, determine the critical (equilibrium)
points, and classify each one as asymptotically stable or unstable.
Draw the phase line, and sketch several graphs of solutions in the
ty-plane.
dy
=
= y(64- y²), -∞<yo<∞
dt
The function y(t) = −8 is
Choose one
The function y(t) = 0 is
Choose one ▾
The function y(t) = 8 is
Choose one
Transcribed Image Text:dy dt The following problem involves an equation of the form = f(y). Sketch the graph of f(y) versus y, determine the critical (equilibrium) points, and classify each one as asymptotically stable or unstable. Draw the phase line, and sketch several graphs of solutions in the ty-plane. dy = = y(64- y²), -∞<yo<∞ dt The function y(t) = −8 is Choose one The function y(t) = 0 is Choose one ▾ The function y(t) = 8 is Choose one
Choose one
an unstable equilibrium solution.
an asymptotically stable equilibrium solution.
a semistable equilibrium solution.
no equilibrium solution at all.
Transcribed Image Text:Choose one an unstable equilibrium solution. an asymptotically stable equilibrium solution. a semistable equilibrium solution. no equilibrium solution at all.
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