C With the additional information that y(n) (0) = 2-n, find the value for ao and write down the solution y(z) you obtain. (For fun: Does this expression look familiar?)
C With the additional information that y(n) (0) = 2-n, find the value for ao and write down the solution y(z) you obtain. (For fun: Does this expression look familiar?)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
help me with c please thank you.
if you dont't know how to do it, can u just pass it to the next expert instead of rejecting ebcause dont know how to do it? thanks
Transcribed Image Text:Consider the second order linear differential equation
for any fixed n = {0, 1, 2, ...}.
a Is zo
=
z²y" (z) + zy' (z) + (z² — n²)y(z) = 0
(4)
O an ordinary point, a regular singular point, or an irregular singular point of
the ODE? Justify your answer.
b. Consider a power series solution around zo
= 0 of the form
∞
y(z) = znΣamzm.
m=0
with ao 0 and fixed n. Solve equation (4) by identifying the coefficients
series. You should be able to find all coefficients as a function of ao.
Am
in the above power
(Hint: substitute the ansatz into the equation and equate coefficients belonging to the same powers
of z, then solve the resulting recurrence relation for the coefficients).
C With the additional information that y(n) (0) = 2¯n, find the value for ao and write
down the solution y(z) you obtain. (For fun: Does this expression look familiar?)
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