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The point x = 0 is a regular singular point of the given differential equation. Find the recu relation for the series solution of the DE below. Show the substitution and all the steps t obtain the recursive relation. Do not solve the equation for y=y(x) xy" + 3y' - xy = 0, 1 a. Cx+1= (k+r+1)(k+r+3) Ck-¹, k≥1 1 b. Ck= (k+r)(2k +2r-1) Ck-2, k22 1 c. Cx===Ck-₁, k21 k+r d. C₁= e. C₁=- <- 1' k+r -Ck-1, k≥1 (k+r)² +5(k+r) 1 (k+r)²-2(k+r)-8 -Ck-2, k≥2

The point x = 0 is a regular singular point of the given differential equation. Find the recu relation for the series solution of the DE below. Show the substitution and all the steps t obtain the recursive relation. Do not solve the equation for y=y(x) xy" + 3y' - xy = 0, 1 a. Cx+1= (k+r+1)(k+r+3) Ck-¹, k≥1 1 b. Ck= (k+r)(2k +2r-1) Ck-2, k22 1 c. Cx===Ck-₁, k21 k+r d. C₁= e. C₁=- <- 1' k+r -Ck-1, k≥1 (k+r)² +5(k+r) 1 (k+r)²-2(k+r)-8 -Ck-2, k≥2

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. Find the recursive relation for the series solution of the DE below. Show the substitution and all the steps to obtain the recursive relation. Do not solve the equation for y=y(x) xy" + 3y' - xy = 0, 1 a. Ck+1²= (k+r+1)(k+r+3) 1 b. Cx = (k+r)(2k+2r-1) Cx-2₁ K²² +2r− Cx-1, k≥ 1 c. Ck = d. e. (k+r+ 1)(k +r+3) k-1, k≥1 1 k+r Ck = - k+r Ck = = (k+r)² +5(k+r) 1 (k+r)²-2(k+r) -8 Ck-1, k21 Ck-2, k≥2
Transcribed Image Text:The point x = 0 is a regular singular point of the given differential equation. Find the recursive relation for the series solution of the DE below. Show the substitution and all the steps to obtain the recursive relation. Do not solve the equation for y=y(x) xy" + 3y' - xy = 0, 1 a. Ck+1²= (k+r+1)(k+r+3) 1 b. Cx = (k+r)(2k+2r-1) Cx-2₁ K²² +2r− Cx-1, k≥ 1 c. Ck = d. e. (k+r+ 1)(k +r+3) k-1, k≥1 1 k+r Ck = - k+r Ck = = (k+r)² +5(k+r) 1 (k+r)²-2(k+r) -8 Ck-1, k21 Ck-2, k≥2
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