? Exercise 1.5.2 The equation dx dy - (y - 5) (y - 1) has two critical points. The smaller critical point is at y = -1 x and it is (stable The larger critical point is at y = -5 x and it is (unstable > Hint Question Help: Message instructor D Post to forum Submit Question Next Page O? Exercise 1.7.3 Here's an example of numerical instability for an equation y'= f(x, y), y(0) = yo. We know y'= -5y, y(0) = 1 has solution y = e-ot. As a increases, y should get closer to zero. Let's use Euler's method with step size h = 1 to approximate y(4). Do the calculations: XO = 0 yo = 1 x1 = xoth= 1 y1 = yo + hf(x0, yo) = - 4 X 2 = with = 2 y2 = y1+ hf(x1, y1) 16 X x3 = x2th = 3 y3 = yz + hf(22, y2) = -64 X 24 = 23 th = 4 y4 = y3 + hf(23, y3) = -256 X Does this give us a good estimate of y(4)? Yes No O O Question Help: Message instructor D Post to forum Submit Question Next Page