Although it might not be obvious from the differential equation, its solution could

Chapter 9, Problem 12

(choose chapter or problem)

Although it might not be obvious from the differential equation, its solution could “behave badly” near a point x at which we wish to approximate y(x). Numerical procedures may give widely differing results near this point. Let y(x) be the solution of the initial-value problem \(y^{\prime}=x^{2}+y^{3}\), y(1) = 1.

(a) Use a numerical solver to graph the solution on the interval [1, 1.4].

(b) Using the step size h = 0.1, compare the results obtained from Euler’s method with the results from the improved Euler’s method in the approximation of y(1.4).

Text Transcription:

y^prime=x^2+y^3

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