Consider a system of two nonlinear first order ODEs where r and y are functions...

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Consider a system of two nonlinear first order ODEs where r and y are functions of the independent variable t 2tanh r 2r cos y 1 3cosh z 3e y sin x 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 z 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 e What type of fixed point is the equilibrium solution r y 0 Sketch the phase portrait of the linear system d Find the solution of the linear system corresponding to the initial conditions z 0 1 y 0 0 Determine the values lim r t and lim y t

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Consider a system of two nonlinear first order ODEs where r and y are functions of the independent variable t 2tanh r 2r cos y 1 3cosh z 3e y sin x 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 z 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 e What type of fixed point is the equilibrium solution r y 0 Sketch the phase portrait of the linear system d Find the solution of the linear system corresponding to the initial conditions z 0 1 y 0 0 Determine the values lim r t and lim y t