Solutions please Consider a system of two nonlinear first-order ODEs, where x and y are functions of theindependent variable t:* = 2 tanh(x) − 2x cos(y) + e*+ 3y - 1, y = 3 cosh(x) - 3e+y+sin(x).11(a) Write down in matrix form of the type X = AX with X = (x, y) the systemobtained by linearisation of the above equations around the point x = y = 0.Specify the elements of the matrix A.(b) Find the eigenvalues and eigenvectors of the matrix A obtained in (a). Writedown the general solution of the linear system.I(c) What type of fixed point is the equilibrium solution x=y=0? Sketch the phaseportrait of the linear system.(d) Find the solution of the linear system corresponding to the initial conditionsx(0) = 1, y(0) = 0. Determine the values limto r(t) and limto y(t).

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Answered: I Consider a system of two nonlinear…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.7: The Inverse Of A Matrix

Problem 31E

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