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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
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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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

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?)
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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