Can you help me to get started in part b? I don't know how to approach this problem. Please ignore the word count requirement.

PROBLEM 2: PART a) Below is an Euler's method approximation with At = 1 for a differential equation dy/dt = f(y) (f is continuously differentiable). Say all you can about the solution with y(0) = 2. (NO MORE THAN 50 WORDS.) PART b) Suppose you do an Euler's method approximation for the solution with y(0) = 1, y(0) = 0 for the system corresponding to the harmonic oscillator dy + 0.01-4 + 2y =0 obtaining the graph below: i) Explain how you know this picture is not an accurate representation of the long-term qualitative behavior of the solution. (AT MOST 20 WORDS). 4 HAA ii) Approximately how much error in the numberical method per time unit can be allowed in the numerical approximations and still see the correct long-term behvior of solutions (you may state your answer using exponentials)