Solve the initial value problem x'(t) = Ax(t) for t≥ 0, with x(0) = (1,4). Classify the nature of the origin as an attractor, repeller, or saddle point of the dynamical system described by x' = Ax. Find the directions of greatest attraction and/or repulsion.-2A-[-]A=10 - 16Solve the initial value problem.x(t) =

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Answered: Solve the initial value problem x'(t) =…

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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Draw the slope fields of dy/dt = -t2y at integer values ( y is greater than or equal to -5 and less than or equal to 5 and x is greater than or equal to -5 and less than or equal to 5). Sketch the solution curves with initial values y(0) = 2 y(0) = -2 y(-4) = 3 y(-4) = -3
Suppose p and q satisfy the system of differential equations dp dt = p(3 − p+q), dq dt = = q (6 - p - q) ● Starting at (6,2), as t increases will (p, q) approach (5.90, 1.94) or (6.10,2.07)? • Fill in the blanks. The equilibrium points of the system are (0, 0), (3,0), (0,0) and (0.
Solve the equation y' - graphically. Below, the graph in the (y, y') plane is shown. 10 (a) Find the equilibrium solutions and classify each as to its stability. (b) Determine where y(t) is increasing. (c) Determine where y(t) is concave up. (d) On the (t, y) plane, sketch the solutions with y(0) = -1, y(0) = 1 and y(0) = 6.
please help show the step on how to get the correct asnwer. i have attached the correct answer Question: solve the given initial-value problem.sketch the graphof both the forcing function and the solution. y″ + y′ +3y = u(t –2)y(0)= 0y′(0) = 1
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y ″ + 4y = sint − u2π(t) sin(t − 2π) with initial condition y ( 0 ) = 0 and y ′(0) = 0 sketch the graph of the forcing function on an appropriate interval.
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The motion of a mass-spring system with damping is governed by y''(t) + 8y'(t) + ky(t) = 0; y(0) = 2, and y'(0) = 0. Find the equation of motion and sketch its graph for k= 14, 16, and 18.

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