Use Euler's method with step size 0.5 to compute the approximate y-values y1, 32, and y3 of the solution of the initial-value problem y' = 1+ 6x-3y, y(1) = 2. 1. y 2. Y 3. Y 4. Y
Use Euler's method with step size 0.5 to compute the approximate y-values y1, 32, and y3 of the solution of the initial-value problem y' = 1+ 6x-3y, y(1) = 2. 1. y 2. Y 3. Y 4. Y
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Use Euler's method with step size 0.5 to compute the approximate y-values y₁, y₂, and y₃ of the solution of the initial-value problem:**
\[
y' = 1 + 6x - 3y, \quad y(1) = 2.
\]
**Options:**
1. \( y₁ = 2.500, \, y₂ = 4.050, \, y₃ = 4.216 \)
2. \( y₁ = 2.500, \, y₂ = 3.801, \, y₃ = 4.966 \)
3. \( y₁ = 2.400, \, y₂ = 3.763, \, y₃ = 4.493 \)
4. \( y₁ = 2.500, \, y₂ = 3.510, \, y₃ = 4.160 \)
5. \( y₁ = 2.500, \, y₂ = 3.750, \, y₃ = 4.625 \)
**Note:**
Euler's method is a numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. The method uses a step-by-step approach to approximate the function's values. In this problem, you start at \( x = 1 \) with an initial value \( y(1) = 2 \), and then use Euler's method with a step size of 0.5 to find subsequent y-values.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9a433dd5-6857-42c0-ae40-09bd40f154d3%2F2ead580a-1cd5-4a51-91ba-715e0f53a223%2Fyaev20m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Use Euler's method with step size 0.5 to compute the approximate y-values y₁, y₂, and y₃ of the solution of the initial-value problem:**
\[
y' = 1 + 6x - 3y, \quad y(1) = 2.
\]
**Options:**
1. \( y₁ = 2.500, \, y₂ = 4.050, \, y₃ = 4.216 \)
2. \( y₁ = 2.500, \, y₂ = 3.801, \, y₃ = 4.966 \)
3. \( y₁ = 2.400, \, y₂ = 3.763, \, y₃ = 4.493 \)
4. \( y₁ = 2.500, \, y₂ = 3.510, \, y₃ = 4.160 \)
5. \( y₁ = 2.500, \, y₂ = 3.750, \, y₃ = 4.625 \)
**Note:**
Euler's method is a numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. The method uses a step-by-step approach to approximate the function's values. In this problem, you start at \( x = 1 \) with an initial value \( y(1) = 2 \), and then use Euler's method with a step size of 0.5 to find subsequent y-values.
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