The graph of the function ?(?)f(x) is (the horizontal axis is x.)Given the differential equation x'(t) = f(x(t)).List the constant (or equilibrium) solutions to this differential equation inincreasing order and indicate whether or not these equilibria are stable, semi-stable, or unstable.

Answered: (the horizontal axis is x.) Given the…

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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Question

The graph of the function ?(?)f(x) is

(the horizontal axis is x.)
Given the differential equation x'(t) = f(x(t)).
List the constant (or equilibrium) solutions to this differential equation in
increasing order and indicate whether or not these equilibria are stable, semi-
stable, or unstable.

Expert Solution

Step 1

Equilibrium points are the points where the function cuts the x-axis.

Look at the graph and find the equilibrium points and correspondingly for each equilibrium point draw the slope field.

To draw the slope field at an equilibrium point, check for the left and right of the equilibrium point. If the velocity that is $x' (t)$ is positive, then the field lines will converge to the equilibrium point and if $x' (t)$ is negative, then the field lines will move away from the equilibrium point.

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