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y = 2xy = 2y = 0)

y = 2xy = 2y = 0)

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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I am stuck on problem 4 we are supposed to convert the n into k and then find a pattern to write an equation and I am just confused.
Problem H y=anx^ АЧ y' = nanx" y": n(n-lanx"ка n(n-1) an x-2 मंजू n(n-1) anx^2 у -Rxy'-2y=0 - k=n-2 K+2=n (к+2) ((k+2)-1) актах (((+2) (k+1) ак+2 по 2x z nanx n 2nank" -- (2k -2 k (k+2)(k+1) n-t со 2 то anx" 2 anx? k а как же - зак х = 0 х х=0 - - з как-2ак) x-o - *(< +2)(k+D ак+2 = а как - 20 к зак ак+2
Transcribed Image Text:Problem H y=anx^ АЧ y' = nanx" y": n(n-lanx"ка n(n-1) an x-2 मंजू n(n-1) anx^2 у -Rxy'-2y=0 - k=n-2 K+2=n (к+2) ((k+2)-1) актах (((+2) (k+1) ак+2 по 2x z nanx n 2nank" -- (2k -2 k (k+2)(k+1) n-t со 2 то anx" 2 anx? k а как же - зак х = 0 х х=0 - - з как-2ак) x-o - *(< +2)(k+D ак+2 = а как - 20 к зак ак+2
i.e. show that: where c is a constant. L{cf +8} = cL{f} + £{8} Problem 2: Use the method of Laplace transforms to solve the IVP: y" - y' - 2y = 10 cost y (0) = 0 (y'(0) = = -1 Problem 3: Find the interval of convergence of the power series: Problem 4: Find two linearly independent power series solutions to the given DE centered at x = 0 of y" - 2xy' - 2y = 0. (2k-2)ak (K+2)(K+1) = ак+2 (3n+ 1)(x-1)" 4n n=0
Transcribed Image Text:i.e. show that: where c is a constant. L{cf +8} = cL{f} + £{8} Problem 2: Use the method of Laplace transforms to solve the IVP: y" - y' - 2y = 10 cost y (0) = 0 (y'(0) = = -1 Problem 3: Find the interval of convergence of the power series: Problem 4: Find two linearly independent power series solutions to the given DE centered at x = 0 of y" - 2xy' - 2y = 0. (2k-2)ak (K+2)(K+1) = ак+2 (3n+ 1)(x-1)" 4n n=0
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