(b) Use Euler's Method with step size h that is a solution to the initial value problem - 1/2 to approximate y(6) for the function y(x) y = 4y, y(3)
(b) Use Euler's Method with step size h that is a solution to the initial value problem - 1/2 to approximate y(6) for the function y(x) y = 4y, y(3)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Solve letter b
![**Euler's Method**
1. **(a)** Use Euler’s Method with step size \( h = 1 \) to approximate values of \( y(2), y(3), y(4) \) for the function \( y(t) \) that is a solution to the initial value problem:
\[
y' = x^2
\]
\[
y(1) = 3
\]
2. **(b)** Use Euler’s Method with step size \( h = \frac{1}{2} \) to approximate \( y(6) \) for the function \( y(x) \) that is a solution to the initial value problem:
\[
y' = 4y
\]
\[
y(3) = \frac{1}{4}
\]
3. **(c)** Use Euler’s Method with step size \( h = \frac{1}{2} \) to approximate \( y(0) \) for the function \( y(t) \) that is a solution to the initial value problem:
\[
y' = 2t - y
\]
\[
y(2) = 2
\]
**Hint:** Your initial condition is after the point you want to estimate to - you'll have to step backwards.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9372b6fe-9d83-4cc3-b9b6-3000d02c5781%2Fa29bd887-2cf1-423c-8fbc-f82d88c3d6b3%2Fyxj5t9h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Euler's Method**
1. **(a)** Use Euler’s Method with step size \( h = 1 \) to approximate values of \( y(2), y(3), y(4) \) for the function \( y(t) \) that is a solution to the initial value problem:
\[
y' = x^2
\]
\[
y(1) = 3
\]
2. **(b)** Use Euler’s Method with step size \( h = \frac{1}{2} \) to approximate \( y(6) \) for the function \( y(x) \) that is a solution to the initial value problem:
\[
y' = 4y
\]
\[
y(3) = \frac{1}{4}
\]
3. **(c)** Use Euler’s Method with step size \( h = \frac{1}{2} \) to approximate \( y(0) \) for the function \( y(t) \) that is a solution to the initial value problem:
\[
y' = 2t - y
\]
\[
y(2) = 2
\]
**Hint:** Your initial condition is after the point you want to estimate to - you'll have to step backwards.
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