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Problem
For Problems 13-18, sketch the phase portrait of the given system for
The system in Problem 7.
For Problems 1-9, determine all equilibrium points of the given system and, if possible, characterize them as centers, spirals, saddles, or nodes.
7.
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Differential Equations and Linear Algebra (4th Edition)
- 1. What is the solution to the system of equations y = 3x – 2 and y =g(x) where g(x) is defined by the function below? y= g(x) 1) {(0,-2)} 2) {(0,-2).(1,6); 3) {(1,6)} 4) {(1,1),(6,16)}arrow_forwardExample 32. Given the following equation for two related markets A and B, find the equilibrium conditions for each market and the price for each market: ► 15PA x, (A) = 82 – 3pA х, (В) %3D 92 + 2pд — 4p; + PB x, (A) = -5 + x, (B) = -6 + 32P, B' where and denote quantity demanded and quantity supplied respectively.arrow_forward8. Find and classify the equilibrium points of the following equations: (9 +x – 3y)x (-8+4x – y)y Discuss the stability of each equilibrium point.arrow_forward
- In Example 1 we used Lotka-Volterra equations to model populations of rabbits and wolves. Let's modify those equations as follows: dR 0.09R(1 0.0001R) - 0.002RW dt dW = = -0.02W+0.00001RW dt Find all of the equilibrium solutions. Enter your answer as a list of ordered pairs (R, W), where R is the number of rabbits and W the number of wolves. For example, if you found three equilibri solutions, one with 100 rabbits and 10 wolves, one with 200 rabbits and 20 wolves, and one with 300 rabbits and 30 wolves, you would enter (100, 10), (200, 20), (300, 30). Do not round fractional answers to the nearest integer. Answer = (0,0)arrow_forward12. (a) Find the solution(s) to the following system of linear equations: -3.r + 2y + 2z = 5, 4y + 4z = 3, -x - 2x + 4y = -2. (b) Let R be the region in the positive quadrant bounded by the straight lines 4.x, and by the hyperbolas xy = 1 and xy = 3. = 2x and (i) Sketch the region R (ii) Define parameters u = in the (u, v)-plane, corresponding to the region R in the (x, y)-plane. y/x and v = xy. Determine and sketch the region S (iii) Hence, using the given change of variables, evaluate the double integral TxY sin )dA. I = x2arrow_forwardIn Example 1 we used Lotka-Volterra equations to model populations of rabbits and wolves. Let's modify those equations as follows: dR = 0.1R(1 – 0.0001R) – 0.003RW dt dW -0.01W + 0.00004RW dt Find all of the equilibrium solutions. Enter your answer as a list of ordered pairs (R, W), where Ris the number of rabbits and W the number of wolves. For example, if you found three equilibrium solutions, one with 100 rabbits and 10 wolves, one with 200 rabbits and 20 wolves, and one with 300 rabbits and 30 wolves, you would enter (100, 10), (200, 20), (300, 30). Do not round fractional answers to the nearest integer. Answer =|arrow_forward
- 1. Wha at is the solution to the system of equations y= 3x-2 and y= g(x) where g(x) is defined by the function below? y=gx) 1) ((0,-2)} 2) ((0,-2).(1.6); 3) {(1,6)} 4) (1,1).(6, 16)}arrow_forwardCan someone help me with what does "express k in terms of the parameters of the system" and how to do it?arrow_forwardQ.3: Suppose that the three points (1.-5), (-1, 1), and (2, 7) lie on the parabola p(x) = ax² +bx + c. (a) Determine a linear system of three equations in three unknowns that must be solved to find a, b, and c. (b) Solve the linear system obtained in part (a) for a, b, and c.arrow_forward
- _7. What term is eliminated the when the equations in the following system are subtracted? x² + y? = 36 x2 – y = 36 [A] x [B] x² [C] ¥ [D]y?arrow_forward6. Find the general solution of the system: sint X+ -2 costarrow_forwardFor the following system: *i = x1 – xỉ + x2 *2 = 3x1 – x2 (a) Find the equilibrium points of the system (b) Using Linearization, determine the stability of the system at each equilibrium point. (c) Using Lyapunov theory show the origin is unstablearrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning