A square piece of plane material occupies the region given by 0 < x< a,0 < y <а.Its temperature U(x, y) satisfiesa²ua²U= 0(Q2)əx²and the boundary conditions (i) U = 0 on x = 0; (ii) U = 0 on x = a;au(ii):= 0 on y = 0.дуa) Use the method of separation of variables to show that (Q2) and theboundary conditions are satisfied byNITX.(nnyU(x,y) = En=1 Cnsin(-coshn=D1aawhere the C, (n= 1,2,3, ...) are constants.b) In the case when U =x on the edge y = a (where Y, is a constant),acalculate C, inorder to show that00240U(x,y) :2 (-1)*1(-1)"+1sinncosh(nn)NITX'coshn=1

Note: As per bartleby instruction when more then one question is given only one has to be answered.…

A square piece of plane material occupies the region given by 0 < x < a, 0 < y< а. Its temperature U(x, y) satisfies a²u = 0 ду? a²u (Q2) and the boundary conditions (i) U = 0 on x = 0; (ii) U = 0 on x = a;

A square piece of plane material occupies the region given by 0 < x < a, 0 < y< а. Its temperature U(x, y) satisfies a²u = 0 ду? a²u (Q2) and the boundary conditions (i) U = 0 on x = 0; (ii) U = 0 on x = a;

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

ChapterA: Appendix

SectionA.2: Geometric Constructions

Problem 10P: A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in...

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Question

A square piece of plane material occupies the region given by 0 < x< a,0 < y <
а.
Its temperature U(x, y) satisfies
a²u
a²U
= 0
(Q2)
əx²
and the boundary conditions (i) U = 0 on x = 0; (ii) U = 0 on x = a;
au
(ii):
= 0 on y = 0.
ду
a) Use the method of separation of variables to show that (Q2) and the
boundary conditions are satisfied by
NITX.
(nny
U(x,y) = En=1 Cnsin(-
cosh
n=D1
a
a
where the C, (n= 1,2,3, ...) are constants.
b) In the case when U =
x on the edge y = a (where Y, is a constant),
a
calculate C, inorder to show that
00
240
U(x,y) :
2 (-1)*1
(-1)"+1
sin
ncosh(nn)
NITX'
cosh
n=1

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