1. Engineering
  2. Mechanical Engineering
  3. for each of the following differential equations 1 xx22x 2...

Question: for each of the following differential equations 1 xx22x 2...

Question details
For each of the following differential equations: 1. x’=x^2-2x
2. x”=x^3-x
3. x”=sin(x)+x

a) find the equilibria
b) use the derivative test to determine whether the equilibria represents sinks or sources
c) sketch the phase line
HW instructions: The answers to each of the following problems are short, and therefore, no partial credit will be awarded. The homework must be submitted to crowdmark You must only submit vour solutions to the problems whose label is surrounded by a box like this: Problem XX: No late submissions will be Problem 1: For each of the following differential equations: accepted. 3. z sin (z) + r (hint: for this problem. plot sin (z) + 1, and observe its zero crossings) (a) Find the equilibria (b) Use the derivative test to determine whether the equilibria represent sinks or sources c)Sketch the phase line Problem 2: Consider the function f(x) shown in the graph below: 1. Sketch the phase line corresponding to the differential equation f() 2. Let g(z) f(az) a. How will the number of equilibria change if the parameter a is allowed to start increasing from an initial value of ? Write down the number of equilibria that correspond to each critical value of a, i.е., values of a where the number of equilibria changes. These values of a represent bifurcation points. f(x) -02 T2
Solution by an expert tutor
Blurred Solution
This question has been solved
Subscribe to see this solution