he point x = 0 is a regular singular point of the given differential equation. Зху" - у' + Зу 3 о how that the indicial roots r of the singularity do not differ by an integer. (List the indicial roots below as a comm st.) se the method of Frobenius to obtain two linearly independent series solutions about x = 0. Form the general sol p, o). 9x3 9x? 9x3 + + ... 8 56 80 880 9x2 = c,( 1 - 3x + 8. 9x3 3x 9x? 9x3 1 - - + 5 ... 56 80 880 9x2 1 + 3x - 9x3 1820 9x3 9x? = c, + + + 4 20 140 x2 x3 x3 x + 4 ... 4 36 36 9x2 = c,( 1 + 3x 4 9x3 3x 9x? 9x3 + ... 20 140 1820
he point x = 0 is a regular singular point of the given differential equation. Зху" - у' + Зу 3 о how that the indicial roots r of the singularity do not differ by an integer. (List the indicial roots below as a comm st.) se the method of Frobenius to obtain two linearly independent series solutions about x = 0. Form the general sol p, o). 9x3 9x? 9x3 + + ... 8 56 80 880 9x2 = c,( 1 - 3x + 8. 9x3 3x 9x? 9x3 1 - - + 5 ... 56 80 880 9x2 1 + 3x - 9x3 1820 9x3 9x? = c, + + + 4 20 140 x2 x3 x3 x + 4 ... 4 36 36 9x2 = c,( 1 + 3x 4 9x3 3x 9x? 9x3 + ... 20 140 1820
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:The point x = 0 is a regular singular point of the given differential equation.
Зху" — у' + 3у %3D0
Show that the indicial roots r of the singularity do not differ by an integer. (List the indicial roots below as a comma-separated
list.)
r =
Use the method of Frobenius to obtain two linearly independent series solutions about x = 0. Form the general solution on
(0, c0).
v C,
9x2
1 - 3x +
9x3
3x
9x2
+
9x3
+...
1 -
8
56
80
880
O y = c, 1 - 3x +
9x2
9x3
9x2
3x
+
1
+
8
56
...
80
880
Oy= C;x(1
9x2
9x3
3x
9x2
+
9x3
+
1 + 3x
+
+
-
...
4
20
7
140
1820
x2
x3
x3
+ CzX
+
1 - x +
+
...
36
...
4
36
O y = c, 1 + 3x -
9x
9x3
9x2
9x3
3x
+
+
+
+
4
20
7
140
1820
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