5. Euler's Method and Error. Consider the initial value problem y = x(1-y) y(0) = 2. (a) We can use separation of variables to find an exact solution y(r)e/2+1 Use this to compute y(x) for x = 1. y(1)= ? Use Euler's method with 2 steps to approximate the solution to the initial value problem for r=1. Y = 1(1-4) Y'=1(14) V=24 e-v²12 e-1212 8+112 Y 6.5 7=2 4(x) = c Compare the exact value of the solution to the approximate value using Euler's method, and compute the error.
5. Euler's Method and Error. Consider the initial value problem y = x(1-y) y(0) = 2. (a) We can use separation of variables to find an exact solution y(r)e/2+1 Use this to compute y(x) for x = 1. y(1)= ? Use Euler's method with 2 steps to approximate the solution to the initial value problem for r=1. Y = 1(1-4) Y'=1(14) V=24 e-v²12 e-1212 8+112 Y 6.5 7=2 4(x) = c Compare the exact value of the solution to the approximate value using Euler's method, and compute the error.
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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5. Euler's Method and Error. Consider the initial value problem
y = x(1-y)
y(0) = 2.
(a)We can use separation of variables to find an exact solution y(x)=2/2+11 Use
this to compute y(x) for x = 1.
y(1)=
?
(Use Euler's method with 2 steps to approximate the solution to the initial value
problem for x=
= 1.
y = 1(1-4)
Y'=1(14)
e-v²rz
e-ize
7
6.5
५९४५ =C
7:2
Compare the exact value of the solution to the approximate value using Euler's
method, and compute the error.
1-4101:2
2-26=C
dx
S(Hp)=dt
1414-(-1104
91 (1-848
your as 1-y
=d+ Iny-In(1-4)=tic
1534
te
(1+2)(=2
(=213
Y = (21312
1+(213)
2
€
Yer-v=ce² (elect
Yence 1) = cet
4-2
(1)
(21 = y+cil
5
et
ING CARD
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