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Use Euler's method with step size h = 0.2 to approxi- mate the solution to the initial value problem 1 y' y² = ² = (y² + y)₂ y(1) = 1 X at the points x = 1.2, 1.4, 1.6, and 1.8.

Use Euler's method with step size h = 0.2 to approxi- mate the solution to the initial value problem 1 y' y² = ² = (y² + y)₂ y(1) = 1 X at the points x = 1.2, 1.4, 1.6, and 1.8.

Calculus For The Life Sciences
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 34CR
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6. Use Euler's method with step size h mate the solution to the initial value problem = 0.2 to approxi- y' = (y² 0? + y). y(1) = 1 | at the points x = 1.2, 1.4, 1.6, аnd 1.8.
Transcribed Image Text:6. Use Euler's method with step size h mate the solution to the initial value problem = 0.2 to approxi- y' = (y² 0? + y). y(1) = 1 | at the points x = 1.2, 1.4, 1.6, аnd 1.8.
8. Use the improved Euler's method subroutine with step 0.2 to approximate the solution to the initial size h value problem y' = {o* +y). 1 y(1) = 1, at the points x = 1.2, 1.4, 1.6, and 1.8. (Thus, input N = 4.) Compare these approximations with those obtained using Euler's method (see Exercises 1.4, Problem 6, page 28).
Transcribed Image Text:8. Use the improved Euler's method subroutine with step 0.2 to approximate the solution to the initial size h value problem y' = {o* +y). 1 y(1) = 1, at the points x = 1.2, 1.4, 1.6, and 1.8. (Thus, input N = 4.) Compare these approximations with those obtained using Euler's method (see Exercises 1.4, Problem 6, page 28).
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The given differential equation is y'=1xy2+y with y1=1.

The given step size is h=0.2.

We know that the nth iteration to solve the differential equation y'=fx,y with step size h using Euler's method is calculated as:

yn+1=yn+hfxn,yn, where xn+1=xn+h.

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