Consider a system of two nonlinear first-order ODEs, where x and y are functions of the independent variable t: * = 2 tanh (x) - 2x cos(y) +e+³y - 1, y = 3 cosh(x) - 3ey + 29 y+sin(x). (a) Write down in matrix form of the type X = AX with X = (x, y)T 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. (c) What type of fixed point is the equilibrium solution x = y = 0? Sketch the phase portrait of the linear system.

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