Solve the following initial-boundary-value problem by using the separation of variables technique: Utt UTI, with the prescribed boundary conditions u(0, t) = 0, u(1, t) = 0, ana une initial conditions where f(x) = a(1-x) 1-a 7 (0 ≤ x ≤1, ,t> 0), ut(x,0) = 0, t>0, 0 < x < 1 u(x,0) = f(x), for 0≤x≤ a, for a ≤x≤ 1, with 0 < a < 1.
Solve the following initial-boundary-value problem by using the separation of variables technique: Utt UTI, with the prescribed boundary conditions u(0, t) = 0, u(1, t) = 0, ana une initial conditions where f(x) = a(1-x) 1-a 7 (0 ≤ x ≤1, ,t> 0), ut(x,0) = 0, t>0, 0 < x < 1 u(x,0) = f(x), for 0≤x≤ a, for a ≤x≤ 1, with 0 < a < 1.
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.
Chapter14: Discrete Dynamical Systems
Section14.3: Determining Stability
Problem 13E: Repeat the instruction of Exercise 11 for the function. f(x)=x3+x For part d, use i. a1=0.1 ii...
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Transcribed Image Text:Solve the following initial-boundary-value problem by using the separation
of variables technique:
Utt = Ugr ,
(0<x < 1, ,t > 0),
with the prescribed boundary conditions
u(0, t) = 0,
u(1,t) = 0,
t > 0,
ana une initial conditions
0 < x < 1
u(x, 0) = 0,
u(x,0) = f(x),
where
x,
for 0<x<a,
f(x) =
with 0<a <1.
for a <x <1,
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