Consider the folowing inial value problem, (1 - )/" + 3zy/ – 15y - 0, v(0) = 0, v'(0) – 3. Note: For each part below you must give your answers in torms of fractions (as appropriate), not decimails. (1) This differental equation has singular points at -1:1 Note: You munt use a semicolon here to separate your answers. (0) Since there is no singular point at a= 0, you can tind a normal power series sokution for y(a) about a = 0, Le., va) - E om a. As part of the solution process you must determine the recurrence relation for the coefficients am. Enter your expression for am+2 "m+2" 国助 am (c) Use your recurrence relation to fill in the blanks below. ag (0) Use your recurrance rolation to fil in the blanka below. 固助1 2 4 固助ao 6/5 as (d) Using your results above and the initial conditions, enter the firat three non-zero terms of the power series solution for y(z). v(=) =
Consider the folowing inial value problem, (1 - )/" + 3zy/ – 15y - 0, v(0) = 0, v'(0) – 3. Note: For each part below you must give your answers in torms of fractions (as appropriate), not decimails. (1) This differental equation has singular points at -1:1 Note: You munt use a semicolon here to separate your answers. (0) Since there is no singular point at a= 0, you can tind a normal power series sokution for y(a) about a = 0, Le., va) - E om a. As part of the solution process you must determine the recurrence relation for the coefficients am. Enter your expression for am+2 "m+2" 国助 am (c) Use your recurrence relation to fill in the blanks below. ag (0) Use your recurrance rolation to fil in the blanka below. 固助1 2 4 固助ao 6/5 as (d) Using your results above and the initial conditions, enter the firat three non-zero terms of the power series solution for y(z). v(=) =
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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Transcribed Image Text:Consider the following initial value problem,
(1- 2)y" + 3=zy' – 15y = 0, v(0) – 0, y(0) = 3.
Note: For each part below you must give your answers in terms of fractions (as appropriate), not decimals.
(a) This differential equation has singular points at
z- -1;1
Note: You must use a semicolon here to separate your answers.
(b) Since there is no singular point at a = 0, you can find a normal power series solution for y(a) about a = 0, i.e.,
v(z) = E am am.
m-0
As part of the solution process you must determine the recurrence relation for the coefficients am. Enter your expression for am+2
"m+2
am
(c) Use your recurrence relation to fill in the blanks below.
az =
2
固國a1.
(0) Use your recurrence relation to fill in the blanks below.
a2
固助 a0
a3 =
a4=
a5
6/5
(d) Using your results above and the initial conditions, enter the first three non-zero terms of the power series solution for y(x).
v(2) =
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