Consider the initial value problems (i) { y = y [y(0) = 1 For each of them, answer the following questions. a) Apply Euler's method with h = 0.2. What estimate do you obtain for y(1)? b) Solve the initial value problem and draw the graph of the solution in the interval [0, 1] c) What is the error for each of the estimates you computed? and == -5x4y² (ii) [y': y(0) = 1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Consider the initial value problems
= y
Sy' =
|y(0) = 1
For each of them, answer the following questions.
a) Apply Euler's method with h = 0.2. What estimate do you obtain for y(1)?
b) Solve the initial value problem and draw the graph of the solution in the interval [0, 1]
c) What is the error for each of the estimates you computed?
(i)
and (ii)
[y' = −5x¹y²
y (0) = 1
Transcribed Image Text:Consider the initial value problems = y Sy' = |y(0) = 1 For each of them, answer the following questions. a) Apply Euler's method with h = 0.2. What estimate do you obtain for y(1)? b) Solve the initial value problem and draw the graph of the solution in the interval [0, 1] c) What is the error for each of the estimates you computed? (i) and (ii) [y' = −5x¹y² y (0) = 1
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