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(20 points) Suppose the following ODE - (1 − x)y" + y = 0 (3) has a power series solution y = Σanx" (4) n=0 around x0 = 0. (a) (12 points) Find the recurrence relation that the coefficients {an} satisfy. (b) (8 points) Express a₂, a3 and 4 in terms of ao and a₁.

(20 points) Suppose the following ODE - (1 − x)y" + y = 0 (3) has a power series solution y = Σanx" (4) n=0 around x0 = 0. (a) (12 points) Find the recurrence relation that the coefficients {an} satisfy. (b) (8 points) Express a₂, a3 and 4 in terms of ao and a₁.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.1: Equations
Problem 62E
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(20 points) Suppose the following ODE - (1 − x)y" + y = 0 (3) has a power series solution y = Σanx" (4) n=0 around x0 = 0. (a) (12 points) Find the recurrence relation that the coefficients {an} satisfy. (b) (8 points) Express a₂, a3 and 4 in terms of ao and a₁.
Transcribed Image Text:(20 points) Suppose the following ODE - (1 − x)y" + y = 0 (3) has a power series solution y = Σanx" (4) n=0 around x0 = 0. (a) (12 points) Find the recurrence relation that the coefficients {an} satisfy. (b) (8 points) Express a₂, a3 and 4 in terms of ao and a₁.
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