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-3 a. an+2 an+1 n+2 (-3)1 (-3)2 b, d. y₁ = 1, y2 = x+ -x² + -x³ + (-3)3 -x² + · ... 2! 3! 4! = - Σ n=1 (-3)n-1x n! = 3 In each of Problems 1 through 11: a. Seek power series solutions of the given differential equation about the given point xo; find the recurrence relation that the coefficients must satisfy. b. Find the first four nonzero terms in each of two solutions y₁ and y2 (unless the series terminates sooner). c. By evaluating the Wronskian W[y1, y2](x0), show that yı and y form a fundamental set of solutions. d. If possible, find the general term in each solution. 2. y" + 3y' = 0, x0 = 0

-3 a. an+2 an+1 n+2 (-3)1 (-3)2 b, d. y₁ = 1, y2 = x+ -x² + -x³ + (-3)3 -x² + · ... 2! 3! 4! = - Σ n=1 (-3)n-1x n! = 3 In each of Problems 1 through 11: a. Seek power series solutions of the given differential equation about the given point xo; find the recurrence relation that the coefficients must satisfy. b. Find the first four nonzero terms in each of two solutions y₁ and y2 (unless the series terminates sooner). c. By evaluating the Wronskian W[y1, y2](x0), show that yı and y form a fundamental set of solutions. d. If possible, find the general term in each solution. 2. y" + 3y' = 0, x0 = 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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-3 a. an+2 an+1 n+2 (-3)1 (-3)2 b, d. y₁ = 1, y2 = x+ -x² + -x³ + (-3)3 -x² + · ... 2! 3! 4! = - Σ n=1 (-3)n-1x n! = 3
Transcribed Image Text:-3 a. an+2 an+1 n+2 (-3)1 (-3)2 b, d. y₁ = 1, y2 = x+ -x² + -x³ + (-3)3 -x² + · ... 2! 3! 4! = - Σ n=1 (-3)n-1x n! = 3
In each of Problems 1 through 11: a. Seek power series solutions of the given differential equation about the given point xo; find the recurrence relation that the coefficients must satisfy. b. Find the first four nonzero terms in each of two solutions y₁ and y2 (unless the series terminates sooner). c. By evaluating the Wronskian W[y1, y2](x0), show that yı and y form a fundamental set of solutions. d. If possible, find the general term in each solution. 2. y" + 3y' = 0, x0 = 0
Transcribed Image Text:In each of Problems 1 through 11: a. Seek power series solutions of the given differential equation about the given point xo; find the recurrence relation that the coefficients must satisfy. b. Find the first four nonzero terms in each of two solutions y₁ and y2 (unless the series terminates sooner). c. By evaluating the Wronskian W[y1, y2](x0), show that yı and y form a fundamental set of solutions. d. If possible, find the general term in each solution. 2. y" + 3y' = 0, x0 = 0
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