Express the system of differential equations in matrix notation. x' = (e ¹)x+ (at + bt³)y y' = (tan t)x+ (csct)y Write the system of equations using matrix notation. Select the correct choice below and fill in the answer box (Type an exact answer.) O A. OB. O C. X' - X y' 0- y y [-] y X' X

Solve the system of first-order linear differential equations. (Use C1 and C2 as constants.) Yı' = 3y1 y2' = Y2 (y1(t), y2(t))

Solve the system of differential equations. 6 -2 - X' = X 2 10 x₁(0) = 18, x₂(0) - 26 x₁ (t) = x₂(t) = 8 =

Write the solution to this problem in digital format please a) Factor the differential operator, and, show its expansion. Identify your solution in another color (for example, red) D3 + 10D² + 25D b) Obtain a null operator and prove its result, for the following expression: х3 (1 — 5х) c) Obtain a null operator and prove its result for the following expression: 4e2x — 10хе2х What is the value of a? What is the value of n? What is the null operator?