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3. Exercise §2.4 #9. (May use any method). Solve the diffusion equation ut = kuzz with the initial condition u(x,0) = x² by the following special method. First show that uz satisfies the diffusion equation with zero initial condition. Therefore, by uniqueness, Uxxx = 0. Integrating this result thrice, obtain u(x, t) = A(t)x² + B(t)x+ C(t). Finally, it's easy to solve for A, B, and C by plugging into the original problem.

3. Exercise §2.4 #9. (May use any method). Solve the diffusion equation ut = kuzz with the initial condition u(x,0) = x² by the following special method. First show that uz satisfies the diffusion equation with zero initial condition. Therefore, by uniqueness, Uxxx = 0. Integrating this result thrice, obtain u(x, t) = A(t)x² + B(t)x+ C(t). Finally, it's easy to solve for A, B, and C by plugging into the original problem.

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.CR: Chapter 11 Review
Problem 12CR
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3. Exercise §2.4 #9. (May use any method). Solve the diffusion equation ut = kuzz with the initial condition u(x,0) = x² by the following special method. First show that urrr satisfies the diffusion equation with zero initial condition. Therefore, by uniqueness, Uxxx = 0. Integrating this result thrice, obtain u(x, t) = A(t)x² + B(t)x+ C(t). Finally, it's easy to solve for A, B, and C by plugging into the original problem.
Transcribed Image Text:3. Exercise §2.4 #9. (May use any method). Solve the diffusion equation ut = kuzz with the initial condition u(x,0) = x² by the following special method. First show that urrr satisfies the diffusion equation with zero initial condition. Therefore, by uniqueness, Uxxx = 0. Integrating this result thrice, obtain u(x, t) = A(t)x² + B(t)x+ C(t). Finally, it's easy to solve for A, B, and C by plugging into the original problem.
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