Consider the initial value problem(a) Solve this problem for the exact solutionwhich has a...

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?