4. Autonnomous equations: Sec 1.6: Autonomous equations Determine which differential equation corresponds to each phase diagram....
Determine which differential equation corresponds to each phase
line. You should be able to state briefly how you know your choices
are correct.5 star if correct
Determine which differential equation corresponds to each phase line You should be able to state briefly how you know your choices are correct E dy/dt = 2y - y^2 dy/dt = y(y - 2) F dy/dt = y^2 | y - 2| B dy/dt = 3y - y^2 A dy/dt = y(2 - y)^2 D dy/dt= 4y - y^3 C dy/dt = y^2 - 3y H dy/dt = y^3 - 4y
(1 point) Use the applet provided to draw a phase portrait for ' = -2x(1 - 2)(2-2) The above equation could represent a model of a population that can become extinct if it drops below a particular critical value. What is this critical value? (1 point) Determine the bifurcation value(s) for the one parameter family k = 0 help (numbers) Determine which differential equation corresponds to each phase line. You should be able to state briefly how you know your...
Problem 3: Insights into Differential Equations a. Consider the differential equation 습 +4 = f(t), where f(t) = e-u, 12 0. Please write the forms of the natural and forced solution for this differential equation. You DO NOT need to solve. (7 points) b. Again consider the differential equation f(t), where f(t) is an input and y(t) is the output (response) of interest. Please write the differential equation in state-space form. (10 points) c. The classical method for solving differential...
i need help writing the matlab code for this!
2. The fourth order differential equation 2.(4) + 3.0" – sin(t)..' + 8x = {2 can be rewritten as the following system of first order equations Ti = 12 = 13 24 = -8.01 + sin(t). 2- 3.03 + t (a) Write an m-file function for the system of differential equations. (1) Solve the system of equations over the interval ( € (0,25) for the initial conditions 21(0) = 1, 12(0)...
*Differential Equations*
Exercise 1.6.2: Draw the phase diagram for different possibilities. Note that these possibilities are A> B, or A B orA and B both complex (i.e. no real soluins). Hint: Fix some simple k and M and then vary h For example, let M-8 and k-0.1. When h-1, then A and B are distinct and positive. The graph we will get is given in Figure 1.10 on the next page. As long as the population starts above B which...
Consider the autonomous differential equation y = f(y) = y4-4 уг = y"(y-2) (y+2). a) (3 points) Find all the equilibrium solutions (critical points). f(y) to determine where solutions are increasing / decreasing. Use the sign of y' e) (3 points) Sketch several solution curves in each region determined by the critical poins in the ty-plane
Consider the autonomous differential equation y = f(y) = y4-4 уг = y"(y-2) (y+2). a) (3 points) Find all the equilibrium solutions (critical points)....
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...
Problem 4. The higher order differential equation and initial conditions are shown as follows: = dy dy +y?, y(0) = 1, y'(0) = -1, "(0) = 2 dt3 dt (a) [5pts. Transform the above initial value problem into an equivalent first order differential system, including initial conditions. (b) [2pts.] Express the system and the initial condition in (a) in vector form. (c) [4pts.] Using the second order Runge Kutta method as follows Ū* = Ūi + hĚ(ti, Ūi) h =...
help with all except numbers 21-26
16. Solve the differential equation by using the Cauchy-Euler Equation 17. Find the solution to the given Initial Value Problem using Green's Theorem 0,y'(0)s 0 y(0) y" + 6y' + 9y x, 18. Find the solution to the given Boundary Value Problem y" ty-1, y(O)0, y(1) 19. Solve the system of differential equations by systematic elimination. dy dt dt 20. Use any procedure in Chapter 4 to solve the differential equation subjected to the...