Use the separation of variables, u(r, 0) = R(r)e(0), to solve the following partial differential equation V²u 1 ə ди 18²u +72 80² (1) in a domain with 1

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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Use the separation of variables, u(r, 0) = R(r)O(8), to solve the following partial differential equation
1 a
v'u =
r Or
1 u
+2 302
(1)
in a domain with 1 <r< 2 and 0 <0 < T. The boundary conditions are
u(1,0) = 0,
u(2,0) = 1
(2)
u(r,0) = 0,
u(r, 7) = 0
(3)
Transcribed Image Text:Use the separation of variables, u(r, 0) = R(r)O(8), to solve the following partial differential equation 1 a v'u = r Or 1 u +2 302 (1) in a domain with 1 <r< 2 and 0 <0 < T. The boundary conditions are u(1,0) = 0, u(2,0) = 1 (2) u(r,0) = 0, u(r, 7) = 0 (3)
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