1. Consider the following linear system of DES.dxdtdydt==3x - 2y4x-6ywhere x(0) = 1, and y(0) = 3.Solve by hand the linear system of DEs with the initial conditions.

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Answered: 1. Consider the following linear system…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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5. Consider the nonlinear system. Sx = -2y + xy ly = x + 4xy (a) Find all the equilibrium points of the nonlinear system, then linearize and classify the linearized systems. (b) Find the solution trajectories as implicit functions of y and x. Use Desmos to graph a bunch of them for different initial conditions. What kind of equilibrium point does the nonlinear system have at (0,0)?
2. For the following coupled system x=y y = x(1-x²)+y find all equilibrium points and determine the nature of the linear system around each of the equilibrium points. Draw the null-clines, directions of the trajectories on each null-clines and hence draw the approximate phase plots the the system.
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QUESTION 3 For the system below a. Find the equilibrium points. b. For the equilibrium point (1,1) solve the associated linear system and perform the qualitative analysis dx dt =x (2-x-y), dy dt = y(y-x²)
C .) Consider the system of differential equations dx dt -Y dy dt x(t) = y(t) = -x. Convert this system to a second order differential equation in y by differentiating the second equation with respect to t and substituting for x from the first equation. Solve the equation you obtained for y as a function of t; hence find x as a function of t. If we also require x(0) = 1 and y(0) = 2, what are x and y?
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Find the general solution Y(t) of the linear system dY/dt = AY, where A = [2 5 -1 4]

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1. Consider the following linear system of DES. dx dt dy dt = = 3x - 2y 4x-6y where x(0) = 1, and y(0) = 3. Solve by hand the linear system of DEs with the initial conditions.