Use the procedure in Example 8 in Section 6.2 to find two power series solutions of the given differential equation about the ordinary point x = 0. y' + e'y' – y = 0 1,3 ܐ ܐܨܐ ܀ Oy=1+ Oy, =1+ 2 Oy =1+ 2 ܐ ܀ ܐ1 ܐ ܐ ܐ ܐ ܡܕܩ ܕܕܢܨ … + ܟ ܕܡܐ ܕ ܕ y .. - ܐܐܐܐ ܥܡܐ ܟܥܫܐX + ܢ -Oy: = 1-x Oy:=1+_x+x + 2 and y2 - X - 3 and y, = x + and y, = x - and y2 - X - +ܐ and y2 = x 4 ܐܨܐ ܐܐ + 13 4 + + - 6 9 + 1x2 + 1x³ + 9 - 1 24 1 24 1 16 1 16
Use the procedure in Example 8 in Section 6.2 to find two power series solutions of the given differential equation about the ordinary point x = 0. y' + e'y' – y = 0 1,3 ܐ ܐܨܐ ܀ Oy=1+ Oy, =1+ 2 Oy =1+ 2 ܐ ܀ ܐ1 ܐ ܐ ܐ ܐ ܡܕܩ ܕܕܢܨ … + ܟ ܕܡܐ ܕ ܕ y .. - ܐܐܐܐ ܥܡܐ ܟܥܫܐX + ܢ -Oy: = 1-x Oy:=1+_x+x + 2 and y2 - X - 3 and y, = x + and y, = x - and y2 - X - +ܐ and y2 = x 4 ܐܨܐ ܐܐ + 13 4 + + - 6 9 + 1x2 + 1x³ + 9 - 1 24 1 24 1 16 1 16
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question

Transcribed Image Text:Use the procedure in Example 8 in Section 6.2 to find two power series solutions of the given differential equation about the ordinary point x = 0.
y' + e'y' – y = 0
1,3
ܐ ܐܨܐ ܀
Oy=1+
Oy, =1+
2
Oy =1+
2
ܠܐܕܐܐܨܐ+Oy
+
+
.…
and y2 - X -
and y, = x +
Oy:=1+_x+x +
2
3
and y, = x -
+ܐ
4
ܡܐ ܠܨ-xܕx- + y+1-:0
ܕܨܐ
y2 X
+ 13
and y2 = x
6
+
ܟܛܚ ܕ - -x- ܕOy -1- o- 3 - .… and y
ܐܐܐܐ
4
9
1
24
-
9
1
24
ܐ ܐ ܐ x- + .…
1
16
1x2 + 1x³ + 1
16
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