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The point x = 0 is a regular singular point of the given differential equation. 3xy" y' + 3y = 0 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, ∞). 9x3 ...) + C₂(1 - 3x + 9x² 7 140 1820 ©y = C₁₂x²/³ (1 © Y = C₂(1₁ 1+ 3x - 1+ 3x - 9x² 4 + 3 9x3 20 9x² 9x3 + 4 20 + ...) + C₂x¹/³(1. 3x 9x² + 7 140 9x³ 1820 +.. +..

The point x = 0 is a regular singular point of the given differential equation. 3xy" y' + 3y = 0 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, ∞). 9x3 ...) + C₂(1 - 3x + 9x² 7 140 1820 ©y = C₁₂x²/³ (1 © Y = C₂(1₁ 1+ 3x - 1+ 3x - 9x² 4 + 3 9x3 20 9x² 9x3 + 4 20 + ...) + C₂x¹/³(1. 3x 9x² + 7 140 9x³ 1820 +.. +..

Advanced Engineering Mathematics
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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The point x = 0 is a regular singular point of the given differential equation. 3xy" - y' + 3y = 0 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, ∞). ...) + c₂(1 9x3 1820 y = C₁x¹4/31 + 3x 1+1/3/1 3 9x² + 9x³ 4 20 + 3x 9x² + 7 140 3x 9x² y = C₁ ( 1 + 3x - 3x² + 3x² + ...) + ₂x¹/²(1 – 20 (1 943 4 20 + 7 140 1820 9x3 Y = C₁₂ (1= x + x² - ² + ... + ₂ x ²²³ ( 1 - x + x ² - 1/2 + ...) y x³ саха 4 36 4 36 + + y = C₁ (1 - 3x + 9x³²9x² + ...) + 5₂x²³ ( 1 - 3/5 + 9x² - 3x3 + ...) 3x 9x³ C₂+4/3 (1 8 56 5 80 880 © y = C₁x¹/² ( 1 - 3x + 3x² - 86² +) + ₂(1 - 3x + 2x² - 30+...) 9x3 (1 ..) 9x3 / 8 56 80 880
Transcribed Image Text:The point x = 0 is a regular singular point of the given differential equation. 3xy" - y' + 3y = 0 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, ∞). ...) + c₂(1 9x3 1820 y = C₁x¹4/31 + 3x 1+1/3/1 3 9x² + 9x³ 4 20 + 3x 9x² + 7 140 3x 9x² y = C₁ ( 1 + 3x - 3x² + 3x² + ...) + ₂x¹/²(1 – 20 (1 943 4 20 + 7 140 1820 9x3 Y = C₁₂ (1= x + x² - ² + ... + ₂ x ²²³ ( 1 - x + x ² - 1/2 + ...) y x³ саха 4 36 4 36 + + y = C₁ (1 - 3x + 9x³²9x² + ...) + 5₂x²³ ( 1 - 3/5 + 9x² - 3x3 + ...) 3x 9x³ C₂+4/3 (1 8 56 5 80 880 © y = C₁x¹/² ( 1 - 3x + 3x² - 86² +) + ₂(1 - 3x + 2x² - 30+...) 9x3 (1 ..) 9x3 / 8 56 80 880
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