Problem 3 (Stewart & Day 7.2.9) For each of autonomous differential equations below, find all equilibria...
Problem 1. For each of the following systems of autonomous differential equations, sketch the nullclines and find the equilibria da dy =y-x2 + 3x-2, a+ b 1000 ,2 1-7 a+b 1100
Problem 1. For each of the following systems of autonomous differential equations, sketch the nullclines and find the equilibria da dy =y-x2 + 3x-2, a+ b 1000 ,2 1-7 a+b 1100
4 Consider the autonomous differential equation y f(v) a) (3 points) Find all the equilibrium solutions (critical points). b) (3 points) Use the sign of y f(z) to determine where solutions are increasing / decreasing. Sketch several solution curves in each region determined by the critical points in c) (3 points) the ty-plane. d) (3 points) Classify each equilibrium point as asymptotically stable, unstable, or semi-stable and draw the corresponding phase line.
4 Consider the autonomous differential equation y f(v)...
Math 2050 Group Assignment 1: Qualitative Analysis of Differential Equations #!Suppose a population grows according to the logistic equation but is subject to a constant per cap harvest rate of h. If N(t) is the population size at time t, the population can be given by the equation dN Different values of h result in different equilibrium population sizes ifh is large enough, we m extinction. a) Suppose r - 2 and K- 1000. Find all equilibria. What va Determine...
Please solve the following problem, solve all parts
3. Consider the following system of autonomous differential equations for the populations of two species: dx dt dy dt --0.2y0.0004 ry 0.1 x 0.001 ry a) What type of system might this represent (and why) ? b) Are there equilibria? If yes, what are they? c) Perform a graphical analysis and sketch some trajectories in the phase plane. Comment on the stability of any equilibria. d) What would you predict for the...
Bifurcation dy Consider the autonomous differential equation =y? - 2y + 8. We will begin by examining dt the equilibrium solutions of the equation for various values of the parameter 8 1. Find the equilibrium solutions of the equation for 8 = -4,-2, 0, 2, 4 and make a sketch of the phase line for each value. Determine the stability of each equilibria. 2. Use a computer or some other means to sketch some solution curves for each value of...
Answer as much as possible please! thank you
4. Qualitative Behavior of Autonomous First Order Differential Equations: Consider the graphs of g(N) in the panels (a) - (d) in Figure 1. For each graph, identify all equilibrium points and classify them as either stable or unstable. Then, for each panel, make a graph of N(t) vs. t for 0<1<oo with the given conditions: (a) N(0)-1; N(0)-3. (b) N(O) 0.5; N(O)2 (c) N(O) 1.5; N(0)3 (d) N(0)0; N(O)1.5 Assume that N2...
(6 points) Find a first-order system of ordinary differential equations equivalent to the second-order ordinary differential equation Y" + 2y' + y = 0. From the system, find all equilibrium solutions, and determine if each equilibrium solution is asymptotically stable, or unstable.
Find an autonomous differential equation with all of the following properties: equilibrium solutions at y=0 and y=3, y' > 0 for 0<y<3 and y' < 0 for -inf < y < 0 and 3 < y < inf dy/dx =
2. Differential equations and direction fields (a) Find the general solution to the differential equation y' = 20e3+ + + (b) Find the particular solution to the initial value problem y' = 64 – 102, y(0) = 11. (e) List the equilibrium solutions of the differential equation V = (y2 - 1) arctan() (d) List all equilibrium solutions of the differential equation, and classify the stability of each: V = y(y - 6)(n-10) (e) Use equilibrium solutions and stability analysis...
1. Consider the family of differential equations dy/dx = y^3 +
ky + k^3 .
Please Help me with it, thanks so much
1. Consider the family of differential equations de set = y2 + ky + k3. (a) Are there any equilibrium solutions when k = 0? If so, what are they? (b) Draw the bifurcation diagram. That is, sketch a graph of the critical values as a function of the parameter k. Clearly label the axes. (You may...