Consider the initial value problem

[math]

  1. Find the eigenvalue [math], an eigenvector [math], and a generalized eigenvector [math] for the coefficient matrix of this linear system.
    [math] , [math]
    [math][math]
    , [math]
    [math][math]


  2. Find the most general real-valued solution to the linear system of differential equations. Use [math] as the independent variable in your answers.
    [math]
    [math] [math]
    [math]
    [math][math]


  3. Solve the original initial value problem.
    [math]
    [math]