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3. (a) Solve the differential equation y" - 9y' + 20y = 0, using the auxiliary poly- nomial (b) Use your answer from part (a) and the Maclaurin series e* = ∞ xn n! to find n=0 two linearly independent power series solutions centered about the ordinary point to 0. Calculate the coefficients for and write the first five terms for each of the two power series solutions. (c) Use the method of 6.2 (Power Series Centered about Ordinary Points) to find two linearly independent power series solutions centered about the ordinary point x0 = 0. Calculate the coefficients for and write the first five terms for each of the two power series solutions.

3. (a) Solve the differential equation y" - 9y' + 20y = 0, using the auxiliary poly- nomial (b) Use your answer from part (a) and the Maclaurin series e* = ∞ xn n! to find n=0 two linearly independent power series solutions centered about the ordinary point to 0. Calculate the coefficients for and write the first five terms for each of the two power series solutions. (c) Use the method of 6.2 (Power Series Centered about Ordinary Points) to find two linearly independent power series solutions centered about the ordinary point x0 = 0. Calculate the coefficients for and write the first five terms for each of the two power series solutions.

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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3. (a) Solve the differential equation y" - 9y' + 20y = 0, using the auxiliary poly- nomial (b) Use your answer from part (a) and the Maclaurin series e* = Σ to find xn n! n=0 two linearly independent power series solutions centered about the ordinary point xo = 0. Calculate the coefficients for and write the first five terms for each of the two power series solutions. (c) Use the method of 6.2 (Power Series Centered about Ordinary Points) to find two linearly independent power series solutions centered about the ordinary point x0 = 0. Calculate the coefficients for and write the first five terms for each of the two power series solutions. (d) Although the two power series solutions in part (b) seem to be different from the two power series solutions in part (c), prove that they are actually the same, in the sense that they generate the same solution space.
Transcribed Image Text:3. (a) Solve the differential equation y" - 9y' + 20y = 0, using the auxiliary poly- nomial (b) Use your answer from part (a) and the Maclaurin series e* = Σ to find xn n! n=0 two linearly independent power series solutions centered about the ordinary point xo = 0. Calculate the coefficients for and write the first five terms for each of the two power series solutions. (c) Use the method of 6.2 (Power Series Centered about Ordinary Points) to find two linearly independent power series solutions centered about the ordinary point x0 = 0. Calculate the coefficients for and write the first five terms for each of the two power series solutions. (d) Although the two power series solutions in part (b) seem to be different from the two power series solutions in part (c), prove that they are actually the same, in the sense that they generate the same solution space.
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