1. Find the equilibrium solutions 2. Determine the stability of each equilibrium solution by using the phase diagram.
1. Find the equilibrium solutions 2. Determine the stability of each equilibrium solution by using the phase diagram.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
For the equation dx/dt = −0.5x + 0.01x2,
1. Find the equilibrium solutions
2. Determine the stability of each equilibrium solution by using the phase diagram.
Expert Solution
Step 1: For Question 1:
To find the equilibrium solutions and determine their stability for the given differential equation:
Find the equilibrium solutions: Equilibrium solutions are the values of x for which (dx/dt) = 0. To find them, set (dx/dt) equal to zero and solve for x:
Now, factor out x:
Setting each factor equal to zero:
a)
b)
Solving for x in equation b:
So, the equilibrium solutions are x = 0 and x = 50.
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