Problem 6. Consider the 2 × 2 system of ODEs, where x(t): and x2(t). x' (t) = = for some real-valued functions x₁(t) (x2(t) -1 10 -2 19) x (1) ' when ☑(0) = ( (a) Find eigenvalues and eigenvectors of corresponding coefficient matrix. Label them clearly. (b) Construct the real-valued general solution of the system given above in Eq. (c) Find the particular solution. For your final answer, write down explicitly the pair of solutions, x1(t) and x2(t), in the box below. (d) x₁(t) = x2(t) = Roughly graph how you would expect the phase portrait of this solution to look (on the x1-x2 axis). You do not need to be precise.