1. Reduce to two ordinary differential equations, one an eigenvalue problem, the other having one initial condition, and find the particular solutions: (a) u= 0 for 00, 1 ar ax (x, 0)% 0, u (0, г) - и(1, 1)-0. at
1. Reduce to two ordinary differential equations, one an eigenvalue problem, the other having one initial condition, and find the particular solutions: (a) u= 0 for 00, 1 ar ax (x, 0)% 0, u (0, г) - и(1, 1)-0. at
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 12CR
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Transcribed Image Text:1. Reduce to two ordinary differential equations, one an eigenvalue problem, the other having
one initial condition, and find the particular solutions:
(a)
ar
ax
0=n-
for 0<x< 1, 1>0,
u(x, 0) 0,
at
и (0, г) — и(1, 1) -0.
%3D
(b)
af
+ 25
at
+ u=0 for 0<x<1, 1>0,
u(x, 0) 0,
au
(0, t) = u(1, r) 0.
ax
auau
ax
u 0 for a <x< b, 0<y < I,
(c)
ayay
u (а, у) — 0,
u(b, y) =0,
u (х, 0) — 0.
S20
au
(d)
at
for 0<x< 1, t>0,
u=0
u(0, t) = 0,
u(1, г) — 0.
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