12. y" − (x + 1)y' - y = 0 O a Ob O O d a. y = a₁ [¹ + ½ x² + ²x¹ + ²x6 + ... ] + a₁ [x + ½ x³ + ½ x5 + ¼ x² + · b. y = a1 + x² + x + 6 1 [√x + 1/² x ²₁ 0 [x + ²/² x ² + 1/² x ³ ·+...+ α₁x₁ c. y = a₁ [1 + + 1/2x² + x3 ¹ + ²/² x ¹ +...] + ao d. y = ax² + x³+x+ + -] + a₂ [\x² + x³ + a1 + ·x³ + +...] 4 += x¹ + x^+] ... ***

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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Related questions
Question
y" - (x + 1)y' - y = 0
12.
a. y = a[1 +
ao
b. y = a₁ [1 +
O a
O b
O C
O d
1
x² + x¹ + ! xº + -] + α₁ [
²
2
6
x + 1²/2²
x² + ²x³ + ÷ x¹ + ---] + α₁ [
.3
X
+
x
x+2x3ܝ
1
·x5 + = x² +
4
• α₁₂/x + ²/² x ²₁
c. y = a₁ [1 + ²x² + x³ + ÷ xª + ··· ] + ao [x + ½ x² + ½ x ³ + ½ x ¹ + -]
+ = x¹ +
4
1
d. y = a₁x² + x³ + x++] + ₂ x ² + ² x ³ + ² x ¹ + -]
...
Transcribed Image Text:y" - (x + 1)y' - y = 0 12. a. y = a[1 + ao b. y = a₁ [1 + O a O b O C O d 1 x² + x¹ + ! xº + -] + α₁ [ ² 2 6 x + 1²/2² x² + ²x³ + ÷ x¹ + ---] + α₁ [ .3 X + x x+2x3ܝ 1 ·x5 + = x² + 4 • α₁₂/x + ²/² x ²₁ c. y = a₁ [1 + ²x² + x³ + ÷ xª + ··· ] + ao [x + ½ x² + ½ x ³ + ½ x ¹ + -] + = x¹ + 4 1 d. y = a₁x² + x³ + x++] + ₂ x ² + ² x ³ + ² x ¹ + -] ...
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