questions below:

Express the system of differential equations in matrix notation. X, = (a + bt3)x + (cos t)y y' = (tan t)x+(e')y E) Write the system of equations using matrix notation. Select the correct choice below and ll in the answer box to complete your choice. (Type an exact answer.) y y y] x! o B =K y X If possible, find the first three nonzero terms in the power series expansion for the product f(x)g(x). 8 f ( x) = e /X = E 1 ni ( 7 x ) n n = 0 OO ( - 1 ) k g(x) = sin 5X = E (2k + 1)! (5x) 2k + 1 k = 0 The power series approximation of f(x)g(x) is (Type an expression that includes all terms up to order 3.)Express the system of differential equations in matrix notation. x" - 7x' +ty-(sint)x = 0 y'"' + 4y" -tex' + 7y'te -tx=0 Which of the following sets of definitions allows the given system to be written as an equivalent system in normal form using only the new variables? OA. X1 =X', X2 = X", X3 = y', X4 = y", X5 = y'"' O B. X1 =X, X2 = X', X3 = y, X4 = y', X5 = y" O C. X1 = X, X2 = X", X3 = y, XA = y'"' OD. X1 = X, X2 = X', X3 = y, X4 = y' Write the system of equations using matrix notation. Select the correct choice below and fill in the answer box to complete your choice. (Type an exact answer.) X2 O A. X3 X3 XA X4 X5 X5 X1 X1 X2 X2 O B. X3 X3 XA XA