Find two power series solutions of the given differential equation about the ordinary point x = 0. y" - (x + 1)y' - y = 0 +4 +5 +8 + Oy₁ = 1 + 0x₁=1--++ Oy₁ = 1 + x ²2. + Oy₁ = 1 + 2 + =1-1/²2 - + Oy₁ = 1 + 12 + .. +... +... and Y2 and and and Y₂ = x + X2² - Y₂ = x + Y2 = x + =X+ x³ and y₂ = x + NXN + ~~~~ T + + |~ 1² | 10 I 3²6 3² / N / N I +

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 16CR
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Find two power series solutions of the given differential equation about the ordinary point x = 0.
y" - (x + 1)y' - y = 0
+4 +5
+8
+
Oy₁ = 1 +
0x₁=1--++
Oy₁ = 1 + x ²2.
+
Oy₁ = 1 + 2 +
=1-1/²2 -
+
Oy₁ = 1
+
12
+ ..
+...
+...
and Y2
and
and
and Y₂ = x + X2² -
Y₂
= x +
Y2
= x +
=X+
x³
and y₂ = x +
NXN
+
~~~~
T
+
+
|~ 1² | 10
I
3²6 3² / N / N
I
+
Transcribed Image Text:Find two power series solutions of the given differential equation about the ordinary point x = 0. y" - (x + 1)y' - y = 0 +4 +5 +8 + Oy₁ = 1 + 0x₁=1--++ Oy₁ = 1 + x ²2. + Oy₁ = 1 + 2 + =1-1/²2 - + Oy₁ = 1 + 12 + .. +... +... and Y2 and and and Y₂ = x + X2² - Y₂ = x + Y2 = x + =X+ x³ and y₂ = x + NXN + ~~~~ T + + |~ 1² | 10 I 3²6 3² / N / N I +
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ISBN:
9780321964038
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