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Mathematical Methods by Pearson
book

Mathematical Methods by Pearson

by E. Rukmangadachari
May 2024
Intermediate to advanced content levelIntermediate to advanced
437 pages
17h 41m
English
Pearson India
Content preview from Mathematical Methods by Pearson
Numerical Solution of Ordinary Differential Equations 9-13
2
34
(0.1)
0.7492 (0.1)( 0.6592) (1.2592)
2!
(0.1) (0.1)
(0.7408) ( 0.7408)
64!
0.6897
=+−+
++−+
=
(10)
Anal
ytical Solution
The given dif
ferential equation
=−
2
/dy dx x y
,
equation (1) can be written as
+=
2
/dy dx y x
which
is a first-order linear equation.
Integrating f
actor
∫∫
==
1
.
pdx dx x
eee
Hence, the
general solution is
22
(22)
xxx x
yecxedxyecx x e=+ =+ +
Initial condition is y = 1 when x = 0 c = 1
The required particular solution is
y = e
x
+ x
2
2x + 2
We have y (0.1) y
1
= 0.9052; y (0.2)
y
2
= 0.8213; y (0.3) y
3
= 0.7492; y (0.4)
y
4
= 0.6897.
The approximate values ...
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Publisher Resources

ISBN: 9781299446557Publisher Website