Verify that the vector X is a solution of the given homogeneous linear system. X' = (3 cos(t) (sin(t)) et sin(t), Writing the system in the form X' = AX for some coefficient matrix A, one obtains the following. For or (30 X' = -2 -2 AX = dx dt dy dt = -2x + 5y - = -2x + 4y; 5 5 cos(t) (3 cos(t) sin(t), 4 1) et, 00 x = X X one has 5 cos(t)

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