If, u=f(x,y) and x=rcos, y=rsin; show that Laplace's Equation 1 0²u a²u + ər² rər 1 ди + r² 0² = 0. อu ² u 0x² Əy² = 0; becomes:

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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If, u=f(x,y) and x=rcos, y=rsin0; show that Laplace's Equation
d²u
1 ди 1 0²u
+ +
ər² rər
r² ao
= : 0.
au
0x²
+
² u
= 0; becomes:
Transcribed Image Text:If, u=f(x,y) and x=rcos, y=rsin0; show that Laplace's Equation d²u 1 ди 1 0²u + + ər² rər r² ao = : 0. au 0x² + ² u = 0; becomes:
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