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Consider a system of two nonlinear first-order ODEs, where x and y are functions of the independent variable t: k=9 tanh(y) — 2x(e* − 1) − r® tanh(y), ỷ (a) Write down in matrix form of the type X = AX with X = (x, y) the system obtained by linearisation of the above equations around the point x = y = 0. Specify the elements of the matrix A. 1 COS X X - 3(exy − 1) − y²ex (b) Find the eigenvalues and eigenvectors of the matrix A find in (a). Write down the general solution of the linear system.

Consider a system of two nonlinear first-order ODEs, where x and y are functions of the independent variable t: k=9 tanh(y) — 2x(e* − 1) − r® tanh(y), ỷ (a) Write down in matrix form of the type X = AX with X = (x, y) the system obtained by linearisation of the above equations around the point x = y = 0. Specify the elements of the matrix A. 1 COS X X - 3(exy − 1) − y²ex (b) Find the eigenvalues and eigenvectors of the matrix A find in (a). Write down the general solution of the linear system.

Advanced Engineering Mathematics
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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Please only answer part B. Please can i get a written working out! Thanks.

Consider a system of two nonlinear first-order ODEs, where x and y are functions of the independent variable t: *=9tanh(y) — 2x(e* − 1) − x tanh(y), ỷ == - COS X X − 3(exy − 1) − y²e™ (a) Write down in matrix form of the type X = AX with X = (x, y) the system obtained 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 find in (a). Write down the general solution of the linear system.
Transcribed Image Text:Consider a system of two nonlinear first-order ODEs, where x and y are functions of the independent variable t: *=9tanh(y) — 2x(e* − 1) − x tanh(y), ỷ == - COS X X − 3(exy − 1) − y²e™ (a) Write down in matrix form of the type X = AX with X = (x, y) the system obtained 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 find in (a). Write down the general solution of the linear system.
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