Here\'s two questions: 1: 2: Use Euler\'s method with step size 0.5 to compute t

Question

Here's two questions:

1:

2:

Use Euler's method with step size 0.5 to compute the approximate y-values of the solution of the initial-value problem y' = 2 - 5x + 2y, y(0) = 2. Consider the differential equation dy/dx = 4x, with initial condition y(0) = 2. Use Euler's method with two steps to estimate y when x = 1: (Be sure not to round your calculations at each step!) Now use four steps: (Be sure not to round your calculations at each step!) What is the solution to this differential equation (with the given initial condition)? y = What is the magnitude of the error in the two Euler approximations you found? Magnitude of error in Euler with 2 steps = Magnitude of error in Euler with 4 steps = By what factor should the error in these approximations change (that is, the error with two steps should be what number times the error with four)? factor = (How close to this is the result you obtained above?)

Explanation / Answer

We have

dy/dx =

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.