Verify that the vector X is a solution of the given homogeneous linear system. dx dt = −2x + 5y dy dt = −2x + 4y; X = 5 cos(t) 3 cos(t) − sin(t) et 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) et, one has X' = AX = . Since the above expressions , 5 cos(t) 3 cos(t) − sin(t) et is a solution of the given system.