Answered: Use Euler's method with step size .25…

Use Euler's method with step size .25 to compute the approximate y-values y1, y2, y3, and y4 of the solution of the initial value problem: y' = -2-2x+4y, y(0) = 5 y1= y2= y3= y4=

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter11: Differential Equations

Section11.CR: Chapter 11 Review

Problem 12CR

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Question

100%

Use Euler's method with step size .25 to compute the approximate y-values y1, y2, y3, and y4 of the solution of the initial value problem:

y' = -2-2x+4y, y(0) = 5

y1=

y2=

y3=

y4=

Expert Solution

Step 1

To find- Use Euler's method with step size 0.25 to compute the approximate y-values $y_{1}, y_{2}, y_{3} and y_{4}$ of the solution of the initial value problem:

$y' = - 2 - 2 x + 4 y, y (0) = 5$

Method Used-

Euler's Method:

The solution of the first order initial value problem $y' = f (x, y), y (x_{0}) = y_{0}$ is given by

$y_{1} = y_{0} + h f (x_{0}, y_{0}) y_{2} = y_{1} + h f (x_{1}, y_{1}) y_{3} = y_{2} + h f (x_{2}, y_{2}) ⋮ y_{n} = y_{n - 1} + h f (x_{n - 1}, y_{n - 1})$