Exercise 2-3: Consider the following ODE: x + 7x + 10x = 0. (a) Solve this ODE by substituting in x(t) = eat and finding roots of the characteristic polynomial. (b) Now, write this second order ODE as a system of first order equations, x = Ax, by intro- ducing a new variable v = x. Solve the linear system by decomposing the matrix A into the eigenvalues and eigenvectors. Hint: computing the inverse of the matrix of eigenvectors is easier if they are not normalized (i.e., both of my eigenvectors have integer entries). (c) For both of the solutions in parts (a) and (b), write down the specific solution for an initial condition x(0) = 1 and (0) = 1. (d) What is the long-time behavior of this system