Consider the initial value problem

(a) Solve this problem for the exact solution

which has an infinite discontinuity at x = 0.

(b) Apply Euler’s method with step size h = 0.15 to approximate this solution on the interval -1 ≦ x ≦ 0.5. Note that, from these data alone, you might not suspect any difficulty near x = 0. The reason is that the numerical approximation “jumps across the discontinuity” to another solution of 7xy' + y = 0 for x > 0.

(c) Finally, apply Euler’s method with step sizes h = 0.03 and h = 0.006, but still printing results only at the original points x = -1.00, -0.85, -0.70, ... , 1.20, 1.35. and 1.50. Would you now suspect a discontinuity in the exact solution?

Transcribed Image Text:

dy 7x dx +y=0, y(-1) = 1.