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Consider a system of two nonlinear first-order ODEs, where x and y are functions of th independent variable t: 1 1 * = 2 tanh (x) - 2x cos(y) + ex+³y − 1, y = 3 cosh(x) − 3eºy + y += sin(x). 2 (a) Write down in matrix form of the type X = AX with X = (x, y) obtained by linearisation of the above equations around the point x = Specify the elements of the matrix A. the system = y = 0. (b) Find the eigenvalues and eigenvectors of the matrix A obtained 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 th independent variable t: 1 1 * = 2 tanh (x) - 2x cos(y) + ex+³y − 1, y = 3 cosh(x) − 3eºy + y += sin(x). 2 (a) Write down in matrix form of the type X = AX with X = (x, y) obtained by linearisation of the above equations around the point x = Specify the elements of the matrix A. the system = y = 0. (b) Find the eigenvalues and eigenvectors of the matrix A obtained 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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Consider a system of two nonlinear first-order ODEs, where x and y are functions of the independent variable t: 1 1 ż = 2 tanh(x) — 2x cos(y) + eº+³v − 1, y = 3 cosh(z) — 3e³y + y + sin(x). x 2 (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 obtained 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: 1 1 ż = 2 tanh(x) — 2x cos(y) + eº+³v − 1, y = 3 cosh(z) — 3e³y + y + sin(x). x 2 (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 obtained in (a). Write down the general solution of the linear system.
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