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2. Seek a power series solution of the form y(x) => ana" to the differential equation n=0 y"(r) – 2ry (x) – 4y(x) = 0, xo = 0. (a) Set-up a recurrence for the cofficients, an. (b) Find the first four terms of two independent power series solutions yı and y2 in such a way that you can write y(x) = aoyi (x) + a1y2(x). (c) Determine the Taylor series of e about the point ro = 0. %3D (Hint: Use the Taylor series for e".) (d) By using Part(c), find the explicit form of y2(r).

2. Seek a power series solution of the form y(x) => ana" to the differential equation n=0 y"(r) – 2ry (x) – 4y(x) = 0, xo = 0. (a) Set-up a recurrence for the cofficients, an. (b) Find the first four terms of two independent power series solutions yı and y2 in such a way that you can write y(x) = aoyi (x) + a1y2(x). (c) Determine the Taylor series of e about the point ro = 0. %3D (Hint: Use the Taylor series for e".) (d) By using Part(c), find the explicit form of y2(r).

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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2. Seek a power series solution of the form y(r) =ana" to the differential equation n=0 y"(r) – 2ry (x) – 4y(x) = 0, xo = 0. (a) Set-up a recurrence for the cofficients, an. (b) Find the first four terms of two independent power series solutions yı and y2 in such a way that you can write y(r) = a0y1(x) + a1y2(x). (c) Determine the Taylor series of e about the point ro = 0. %3D (Hint: Use the Taylor series for e".) (d) By using Part(c), find the explicit form of y2(x).
Transcribed Image Text:2. Seek a power series solution of the form y(r) =ana" to the differential equation n=0 y"(r) – 2ry (x) – 4y(x) = 0, xo = 0. (a) Set-up a recurrence for the cofficients, an. (b) Find the first four terms of two independent power series solutions yı and y2 in such a way that you can write y(r) = a0y1(x) + a1y2(x). (c) Determine the Taylor series of e about the point ro = 0. %3D (Hint: Use the Taylor series for e".) (d) By using Part(c), find the explicit form of y2(x).
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