x" +5 t (x')² + 3x = e', x(0) = 1, x'(0) = 2 Using the Euler method with a time step of At=0.2 approximate x(0.6). Do your calculations to at least 4 decimal places of accuracy.
x" +5 t (x')² + 3x = e', x(0) = 1, x'(0) = 2 Using the Euler method with a time step of At=0.2 approximate x(0.6). Do your calculations to at least 4 decimal places of accuracy.
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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2) Please solve the following,
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![**Question 2**
Given the differential equation:
\[ x'' + 5t(x')^2 + 3x = e^t \]
Initial conditions:
\[ x(0) = 1, \]
\[ x'(0) = 2 \]
Using the Euler method with a time step of \(\Delta t = 0.2\), approximate \(x(0.6)\). Perform all calculations to at least 4 decimal places of accuracy.
(Note: There are no graphs or diagrams in this image.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F17facbba-2b30-49af-b629-17c601c4bf12%2F3e4a802f-66cb-423e-8658-963abd91a8cc%2F7iuhhip_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 2**
Given the differential equation:
\[ x'' + 5t(x')^2 + 3x = e^t \]
Initial conditions:
\[ x(0) = 1, \]
\[ x'(0) = 2 \]
Using the Euler method with a time step of \(\Delta t = 0.2\), approximate \(x(0.6)\). Perform all calculations to at least 4 decimal places of accuracy.
(Note: There are no graphs or diagrams in this image.)
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