Consider the initial value problem: y' (t) = t - y², y(3) = 1. stimate y(5) using Euler's method with a step size h = 0.5. ti to: = Yi Yo = y₁ = t₁ = y² % = Yi+1 = Yi Y₁ =

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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Consider the initial value problem:
y' (t) = t - y²,
y(3) = 1.
Estimate y(5) using Euler's method with a step size h = 0.5.
ti
to =
t₁ =
t₂ =
Yi
Yo =
Y₁ =
Y2 =
y₁ = t₁ = y²
% =
y₁ =
Y₂ =
Yi+1 = Yi+h+y₁
Y₁ =
Y2 =
Y3 =
Transcribed Image Text:Consider the initial value problem: y' (t) = t - y², y(3) = 1. Estimate y(5) using Euler's method with a step size h = 0.5. ti to = t₁ = t₂ = Yi Yo = Y₁ = Y2 = y₁ = t₁ = y² % = y₁ = Y₂ = Yi+1 = Yi+h+y₁ Y₁ = Y2 = Y3 =
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How is the y value determined, like y1,y2,y3, and y4? (the second column of the table)

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