Consider the initial value problem on the interval [0, 1]. y' = 4y - x y(0) = 1 (a) Use Euler's method with step size h = 0.2 to approximate the solution of the initial value problem over the given interval. (Round your answers to four decimal places.) y(0.2) 1.8 y(0.4) 2.6 y(0.6) 3.4 y(0.8) 4.2 y(1) = 5 = = = = X X X X (b) Use Euler's method with step size h = 0.1 to approximate the solution of the initial value problem over the given interval. (Round your answers to four decimal places.) y(0.1) = y(0.2) = y(0.3) = y(0.4) = y(0.5) = y(0.6) y(0.7) = y(0.8) y(0.9) = y(1) = =
Consider the initial value problem on the interval [0, 1]. y' = 4y - x y(0) = 1 (a) Use Euler's method with step size h = 0.2 to approximate the solution of the initial value problem over the given interval. (Round your answers to four decimal places.) y(0.2) 1.8 y(0.4) 2.6 y(0.6) 3.4 y(0.8) 4.2 y(1) = 5 = = = = X X X X (b) Use Euler's method with step size h = 0.1 to approximate the solution of the initial value problem over the given interval. (Round your answers to four decimal places.) y(0.1) = y(0.2) = y(0.3) = y(0.4) = y(0.5) = y(0.6) y(0.7) = y(0.8) y(0.9) = y(1) = =
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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Question
![Consider the initial value problem on the interval [0, 1].
y' = 4y - x
y(0) = 1
(a) Use Euler's method with step size h = 0.2 to approximate the solution of the initial value problem over the given interval. (Round your answers to four decimal places.)
y(0.2)
y(0.4)
y(0.6)
y(0.8)
y(1)
1.8
= 2.6
=
= 3.4
= 4.2
= 5
=
(b) Use Euler's method with step size h = 0.1 to approximate the solution of the initial value problem over the given interval. (Round your answers to four decimal places.)
y(0.1)
y(0.2)
y(0.3)
=
=
y(0.4)
y(0.5) =
y(0.6)
y(0.7)
y(0.8)
y(0.9)
y(1)
=
=
ANN
=
=
=
=
X
X
X
X](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F917c3cf7-da96-4e64-810e-7329b2355bb0%2Ffd5934c9-71c1-44e9-bbc3-2b4cf19b2cef%2F3loroyi_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the initial value problem on the interval [0, 1].
y' = 4y - x
y(0) = 1
(a) Use Euler's method with step size h = 0.2 to approximate the solution of the initial value problem over the given interval. (Round your answers to four decimal places.)
y(0.2)
y(0.4)
y(0.6)
y(0.8)
y(1)
1.8
= 2.6
=
= 3.4
= 4.2
= 5
=
(b) Use Euler's method with step size h = 0.1 to approximate the solution of the initial value problem over the given interval. (Round your answers to four decimal places.)
y(0.1)
y(0.2)
y(0.3)
=
=
y(0.4)
y(0.5) =
y(0.6)
y(0.7)
y(0.8)
y(0.9)
y(1)
=
=
ANN
=
=
=
=
X
X
X
X
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