Find the temperature u(x, t) for the boundary-value problem dx² = ди at' 0 < x < L, t> 0 u(0, t) = 0, u(L, t) = 0, t > 0 u(x, 0) = f(x), 0 < x < L when L = 1 and f(x) = 100 sin(67x). [Hint: Look closely at Un = X(x)T(t) = A„e-k(n²77²/L³)t sin(17x) u(x, t) = and u(x, 0) = f(x) = A sin(N7T x).]

Find the temperature u(x, t) for the boundary-value problem dx² = ди at' 0 < x < L, t> 0 u(0, t) = 0, u(L, t) = 0, t > 0 u(x, 0) = f(x), 0 < x < L when L = 1 and f(x) = 100 sin(67x). [Hint: Look closely at Un = X(x)T(t) = A„e-k(n²77²/L³)t sin(17x) u(x, t) = and u(x, 0) = f(x) = A sin(N7T x).]

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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