Construct an appropriate diagonalizing matrix decouple the

Question

Problem in differential equations and linear algebra

EXERCISE 1: Use the Euler-Lagrange Method or Integrating Factor Method to find the general solution to dx/dt = 3x + 2c₂e^-2t and use it to form the general solution to the partially decoupled system.

EXERCISE 2: Construct an appropriate diagonalizing matrix, decouple the linear system, the solve it.

x^- = 

EXERCISE 3: Construct an appropriate diagonalizing matrix, decouple the linear system, then solve the nonhomogeneous system.

x^- =

Attachment:- DecouplingSystems.pdf