2. Consider the nonlinear system of differential equations dx dy = x²y – xy dt = y – e* dt (a) Determine all critical points of the system. (b) For each critical point not on the y-axis: i. Determine the linearisation of the system with the critical point translated to (0,0) and discuss whether it can be used to approximate the behaviour of the non-linear system. ii. Find the general solution of the linearised system using eigenvalues and eigenvectors.

2. Consider the nonlinear system of differential equations dx dy = x²y – xy dt = y – e* dt (a) Determine all critical points of the system. (b) For each critical point not on the y-axis: i. Determine the linearisation of the system with the critical point translated to (0,0) and discuss whether it can be used to approximate the behaviour of the non-linear system. ii. Find the general solution of the linearised system using eigenvalues and eigenvectors.

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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Question

2. Consider the nonlinear system of differential equations
dx
dy
= x²y – xy
dt
= y – e*
dt
(a) Determine all critical points of the system.
(b) For each critical point not on the y-axis:
i. Determine the linearisation of the system with the critical point translated to (0,0) and
discuss whether it can be used to approximate the behaviour of the non-linear system.
ii. Find the general solution of the linearised system using eigenvalues and eigenvectors.

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