In Problems 1-12 proceed as in Example 1 to solve the given boundary-value problem.
5. Solve the boundary-value problem
u(0, t) = 0, u(1, t) = 0, t > 0
u(x, 0) = f(x), 0 < x < 1.
The partial differential equation is a form of the heat equation when heat is generated within a thin rod from radioactive decay of the material.
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Chapter 12 Solutions
Differential Equations with Boundary-Value Problems (MindTap Course List)
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