1. Use the separation of variables, u(r, 0) = R(r)O(0), to solve the following partial differential equationdu1 duV²u+dr(1)=- -r drin a domain with 1 < r < 2 and 0 < 0 < a. The boundary conditions areu(1, 0) = 0,u(2, 0) = 1(2)u(r,0) = 0,u(r, 7) = 0(3)

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1. Use the separation of variables, u(r,0) = R(r)O(0), to solve the following partial differential equation 1 Pu 1 a du r ðr l"ər+D0² = 0 V²u = (1) in a domain with 1< r < 2 and 0 < 0 < a. The boundary conditions are u(2, 0) = 1 u(r, a) = 0 u(1,0) = 0, (2) u(r,0) = 0, (3)

1. Use the separation of variables, u(r,0) = R(r)O(0), to solve the following partial differential equation 1 Pu 1 a du r ðr l"ər+D0² = 0 V²u = (1) in a domain with 1< r < 2 and 0 < 0 < a. The boundary conditions are u(2, 0) = 1 u(r, a) = 0 u(1,0) = 0, (2) u(r,0) = 0, (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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

1. Use the separation of variables, u(r, 0) = R(r)O(0), to solve the following partial differential equation
du
1 du
V²u
+
dr
(1)
=- -
r dr
in a domain with 1 < r < 2 and 0 < 0 < a. 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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