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Q3. The direct solution to following ODE is y = 1/(1+4e-2). Use Euler's method to compute approximate values for ten steps and compute error (difference between true value and approximate value). Use h 0.1 and y(0) = 0. dy dx = (y + x)²

Q3. The direct solution to following ODE is y = 1/(1+4e-2). Use Euler's method to compute approximate values for ten steps and compute error (difference between true value and approximate value). Use h 0.1 and y(0) = 0. dy dx = (y + x)²

Advanced Engineering Mathematics
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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Q3. The direct solution to following ODE is y = 1/(1+4e¯). Use Euler's method to compute approximate values for ten steps and compute error (difference between true value and approximate value). Use h = 0.1 and y(0) = 0. dy dx (y + x)²
Transcribed Image Text:Q3. The direct solution to following ODE is y = 1/(1+4e¯). Use Euler's method to compute approximate values for ten steps and compute error (difference between true value and approximate value). Use h = 0.1 and y(0) = 0. dy dx (y + x)²
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Step 1: Method

Here Eular method formula is y subscript n plus 1 end subscript equals y subscript n plus h f left parenthesis x subscript n comma y subscript n right parenthesis where f left parenthesis x comma y right parenthesis equals left parenthesis x plus y right parenthesis squared.

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