Answered: Solve the IVP by a power series showing…

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Solve the IVP by a power series showing details of your work. Find the value of the sum at x1 to 6 sign

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter9: Sequences, Probability And Counting Theory

Section9.4: Series And Their Notations

Problem 10TI: Determine whether the sum of the infinite series is defined. 24+(12)+6+(3)+

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Question

100%

Solve the IVP by a power series showing details of your work. Find the value of the sum at x1
to 6 significant figures (6S)

(x2 + 2) y” + 3 x y’ - y = 0 y (0) = 1 y’ (0) = 1 x1 = 0.5

Expert Solution

Step 1

Given: IVP is $(x^{2} + 2) y'' + 3 x y' - y = 0$ , $y (0) = 1$ , $y' (0) = 1$ and $x_{1} = 0.5$ .

To solve the IVP by a power series substitution is used.

$y = \sum_{n = 0}^{\infty} a_{n} x^{n}$ , $y' = \sum_{n = 1}^{\infty} n a_{n} x^{n - 1}$ , and $y'' = \sum_{n = 2}^{\infty} n (n - 1) a_{n} x^{n - 2}$

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