Verify that the vector X is a solution of the given homogeneous linear system. dx _- 2x + 5y dt dy -2x + 4y; X = 5 cos(t) 3 cos(t) - sin(t) et dt Writing the system in the form X' = AX for some coefficient matrix A, one obtains the following. X'= X For 5 cos(t) 3 cos(t) - sin(t) er, one has X'= ---Select- are equal AX are linearly independent differ only by a constant 5 cos(t) Since the above expressions | ---Select--- e is a solution of the given system. 3 cos(t) - sin(t)