5. u is defined on {(x, y)|x² +ỷ < 1} and u +u =0 where u=2(x+y)% on {(x, y)|r² + ỷ = 1}. Find u as a polynomial in r, y. -u. 00 Hint 1: In polar coordinates, u(r, 0)=a,+E [4," cos(nt)+b,r" sin(nt)] where n= 1 a, b, are the Fourier coefficients of f(0) :=u(1, 0). Hint 2: cos(30)= 4(cos 0)³ – 3cos0, sin(30)=3sin0 – 4(sin0)³.
5. u is defined on {(x, y)|x² +ỷ < 1} and u +u =0 where u=2(x+y)% on {(x, y)|r² + ỷ = 1}. Find u as a polynomial in r, y. -u. 00 Hint 1: In polar coordinates, u(r, 0)=a,+E [4," cos(nt)+b,r" sin(nt)] where n= 1 a, b, are the Fourier coefficients of f(0) :=u(1, 0). Hint 2: cos(30)= 4(cos 0)³ – 3cos0, sin(30)=3sin0 – 4(sin0)³.
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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![5. u is defined on {(r, y)|x² +y} s 1} and u+uy =0 where u=2(x+y)% on
{(r, y)|r² + f = 1}. Find u as a polynomial in r, y.
00
Hint 1: In polar coordinates, u(r, 6)=q,+E [4"cos(n®)+b,r" sin(n6)] where
n=1
an, b, are the Fourier coefficients of f(8) :=u(1,0).
Hint 2: cos(30)= 4(cos 0)³ – 3cos 0, sin(30)=3 sin 0 – 4(sin0)³.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4bba3fcc-01db-410a-a86c-d766584e6d07%2F3421ad0d-2899-446f-a33c-256daa037e47%2F2fvfwdq_processed.png&w=3840&q=75)
Transcribed Image Text:5. u is defined on {(r, y)|x² +y} s 1} and u+uy =0 where u=2(x+y)% on
{(r, y)|r² + f = 1}. Find u as a polynomial in r, y.
00
Hint 1: In polar coordinates, u(r, 6)=q,+E [4"cos(n®)+b,r" sin(n6)] where
n=1
an, b, are the Fourier coefficients of f(8) :=u(1,0).
Hint 2: cos(30)= 4(cos 0)³ – 3cos 0, sin(30)=3 sin 0 – 4(sin0)³.
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