Suppose that y1 (t) = 11 and y2 (t) = 14 are the only equilibrium solutions of y' = f(y) , and furthermore any solution of this differential equation exists for all t. If f(13) < 0, then for any solution y(t) with 11 < y(0) < 14 we must have that (a) lim y(t) t+ 00 (b) lim y(t) t - 00

Suppose that y1 (t) = 11 and y2 (t) = 14 are the only equilibrium solutions of y' = f(y) , and furthermore any solution of this differential equation exists for all t. If f(13) < 0, then for any solution y(t) with 11 < y(0) < 14 we must have that (a) lim y(t) t+ 00 (b) lim y(t) t - 00

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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Suppose that y1 (t) = 11 and y2(t) = 14 are the only equilibrium solutions of y' = f(y), and
furthermore any solution of this differential equation exists for all t. If f(13) <0, then for any
solution y(t) with 11 < y(0) < 14 we must have that
(a) lim y(t)
t+ 00
(b) lim
y(t)
%3D
t - 00

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