Consider the system of first-order ODES y' (t) = Ay(t), Y1 where A is a 2 x 2 matrix with real-valued entries and y = Yo

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Consider The System Of First Order Odes Y T Ay T Y1 Where A Is A 2 X 2 Matrix With Real Valued Entries And Y Yo 1 (87.86 KiB) Viewed 16 times

Consider the system of first-order ODES y' (t) = Ay(t), Y1 where A is a 2 x 2 matrix with real-valued entries and y = You are given that one of the eigenvalues of A is 11 = -4+3 i and the corresponding eigenvector is 31 1- [] = Two linearly independent solutions are |3e-44 Oy1 = -3e-4t sin(3t) 5e-4t cos(3t) and Y2 = cos(3t) 5e-4t sin(3 t) -3e3t sin(4t) Oy1 = 3e3t cos(41) -5e3t sin(4t) and y2 Oy1 = [ 3e-4t 5e-4t cos(3) sin(3t) and Y2 = Зе -4t sin(3t) 5e-4t cos(3t). [ 3e-44 cos(3 t) Oyi = 5e -40 cos(3) and y2 = 3e -4t sin(3t) 5e-4t sin(3t) Oyj = 3e3t cos(4t) 5e3t cos(4t). and Y2 = -3e3t sin(4t) -5e3t sin(4t) [ 3e3t sin(4t) O y1 = 5e3t cos(4t) and Y2 3e3t cos(4t) -5e3t sin(4t)