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 dxxy
,
equation (1) can be written as
+=
2
/dy dxyx
which
is a first-order linear equation.
Integrating f
actor
∫∫
==
1
.
pdxdxx
eee
Hence, the
general solution is
22
(22)
xxxx
yecxedxyecxxe=+⇒=+−+
∫
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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