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3. a. Solve the following initial boundary value problem for the heat equation ди Ət J²u = D მე2 " 00 u(x, 0) = f(x) u(0,t) = u(L,t) = 0, t>0, 9пх when f(x) = 6 sin L b. Solve the following initial boundary value problem for the diffusion equation ди J²u Ət = D მე2 " 00 u(x, 0) = f(x) Əx = ди მე (L,t) = 0, t>0, ди (0, t): 0, x

3. a. Solve the following initial boundary value problem for the heat equation ди Ət J²u = D მე2 " 00 u(x, 0) = f(x) u(0,t) = u(L,t) = 0, t>0, 9пх when f(x) = 6 sin L b. Solve the following initial boundary value problem for the diffusion equation ди J²u Ət = D მე2 " 00 u(x, 0) = f(x) Əx = ди მე (L,t) = 0, t>0, ди (0, t): 0, x

Calculus For The Life Sciences
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
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 59E: According to the solution in Exercise 58 of the differential equation for Newtons law of cooling,...
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Please solve the following by hand and without the use of AI. Please be thorough and use detailed mathematical formulas to solve. Thank you.

3. a. Solve the following initial boundary value problem for the heat equation ди Ət J²u = D მე2 " 0<x<L, t>0 u(x, 0) = f(x) u(0,t) = u(L,t) = 0, t>0, 9пх when f(x) = 6 sin L b. Solve the following initial boundary value problem for the diffusion equation ди J²u Ət = D მე2 " 0<x<L, t>0 u(x, 0) = f(x) Əx = ди მე (L,t) = 0, t>0, ди (0, t): 0, x <L/2 1, x L/2. = when f(x)=
Transcribed Image Text:3. a. Solve the following initial boundary value problem for the heat equation ди Ət J²u = D მე2 " 0<x<L, t>0 u(x, 0) = f(x) u(0,t) = u(L,t) = 0, t>0, 9пх when f(x) = 6 sin L b. Solve the following initial boundary value problem for the diffusion equation ди J²u Ət = D მე2 " 0<x<L, t>0 u(x, 0) = f(x) Əx = ди მე (L,t) = 0, t>0, ди (0, t): 0, x <L/2 1, x L/2. = when f(x)=
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