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.

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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Question

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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