Consider the following initial value problem: y 0 = e x−y , 0 ≤ x ≤ 1, y(0) = 0, h = 0.5, actual solution: Y (x) = 1 5 x exp (3x) − 1 25 exp (3x) + 1 25 exp (−2x), (a)Use the Euler method to approximate the solutions of initial-value problem, and compare the results to the actual values,

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Consider the following initial value problem:
y
0 = e
x−y
, 0 ≤ x ≤ 1, y(0) = 0, h = 0.5,
actual solution: Y (x) = 1
5
x exp (3x) −
1
25
exp (3x) + 1
25
exp (−2x),

(a)Use the Euler method to approximate the solutions of initial-value problem, and compare the results to
the actual values,
(b)
Use the Heuns method to approximate the solutions of initial-value problem, and compare the results to
the actual values,
(c)
Use the Runge-Kutta method of order four to approximate the solutions of initial-value problem, and
compare the results to the actual values, 

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