B8. Consider the following system of differential equationsi = (X – 1)x + yý = x – y+xz + yzż = -z + a? + y?where A is a real parameter.(a) Find the value of A that any bifurcation occurs for this system near the origin.

For the solution follow the nezt steps.

Answered: B8. Consider the following system of…

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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3.b Plot the first canonic form diagram of the system described by the following differential equation. 2y"(t)-y(1)+2y(t)=-4x"(t) + x'(t)+3x(1)
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Represent the following system of differential equation as Block Diagram. Assume all initial conditions to be zero. * + 3x + 2x + 3y = f(t) ỳ + 4x + 2y = 0
1. Consider the following partial differential equation: du (T,y) -3 (r, y) + 2u(r, y) = 0....(E). Let a and b be two real numbers. For which values of a and b, the function u(x, y) = f(y)ear + g(y)eb" is a solution of (E), where f(y), g(y) are two arbitrary functions. a) a = 2 and b = 3 b) a = 1 and b= 2 c) a = -2 and b = -1 d) None of the above. 2. Using the characteristic method, the solution of the following partial differential equation: |ru + (y+1)uy = u |u(x,0) = f(x), %3D where f is a given function. a) u(r, y) = (y + 1)f ( b) u(x, y) = (y² + 1)f( ). c) u(r, y) = f() d) None of the above. 3. The partial differential equation uz.Urr+ Urr.Uyy – u -r = 0 is a) Second order quasi-linear non-homogenous equation. b) Second order quasi-linear homogenous equation. c) Second order homogenous linear equation. d) None of the above.
Solve the linear system of equations using Differential Operator method.. show details... 2x'+y'+x+5y3D4t x'+y'+2x+2y3D2 LTMIEditor
1. (a) Find the first order partial differential equation by eliminating the arbitrary function f, satisfied by, u(x, y) = xy+ f(x +y). [6 Marks] (b) Find the first order partial differential equation by eliminating the arbitrary constants a and b, satisfied by, u(x, y) = (x +a)(y+b). [6 Marks]
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ty'''+2y''+y'+ty=0 What is the Wronskian of linearly independent solutions?
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B8. Consider the following system of differential equations i = (A – 1)x + Y ý = x – y+xz + yz ż = -z + x² + y² where X is a real parameter. (a) Find the value of X that any bifurcation occurs for this system near the origin.