5. Find all analytic functions f such that Ref + Im f = ry.
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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Just do 5
![5. Find all analytic functions f such that Ref + Im f = xy.
6. Suppose that u is a harmonic function and that vis a harmonic conjugate of u. Show that
ди
ди
Ә
Ju ди
+u
21 ( 1 - ) - 57 (
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Transcribed Image Text:5. Find all analytic functions f such that Ref + Im f = xy.
6. Suppose that u is a harmonic function and that vis a harmonic conjugate of u. Show that
ди
ди
Ә
Ju ди
+u
21 ( 1 - ) - 57 (
дх
дх
дг
ду дх
![ev
B) ANALYTIC AND HARMONIC FUNCTIONS
4. a) v = 3x²y-y³+y²+y-z²+C, CER,
b) v = 2xy + C, CER,
c) v = -cosh a cos y + C,
CER
f(2)=(2²+C), CER.
8. f(z)= az+bz², a,b € C.
d) v = e(y siny-rcos y) + C, CER,
e) v = n(2² + y²) + C, CER
1
9. f(z) = 2³+iaz² + bz+ic, a, b, c € R.
10. f(2)= ae+ib, a € C, bER.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe0d0eb9b-5ed0-46d3-a032-d4bf7a7245ca%2Fc2d5e3d2-5def-4da7-8885-8be04dff2b94%2Fmma78rp_processed.png&w=3840&q=75)
Transcribed Image Text:ev
B) ANALYTIC AND HARMONIC FUNCTIONS
4. a) v = 3x²y-y³+y²+y-z²+C, CER,
b) v = 2xy + C, CER,
c) v = -cosh a cos y + C,
CER
f(2)=(2²+C), CER.
8. f(z)= az+bz², a,b € C.
d) v = e(y siny-rcos y) + C, CER,
e) v = n(2² + y²) + C, CER
1
9. f(z) = 2³+iaz² + bz+ic, a, b, c € R.
10. f(2)= ae+ib, a € C, bER.
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