9.7 Consider the initial value problem y''= y

for t 0, with initial values y(0) = 1 and y'(0) = 2.

(a) Express this second-order ODE as an equivalent system of two first-order ODEs.

(b) What are the corresponding initial conditions for the system of ODEs in part a?

(c) Is this a stable system of ODEs? (d) Perform one step of Eulers method for this

ODE system using a step size of h = 0.5. (e) Is Eulers method stable for this problem

using this step size?

(f ) Is the backward Euler method stable for this problem using this step size?