The equation utt + cut + ku = a2 uxx + F(x, t), (i) where a2 > 0, c 0, and k 0 are
Chapter 11, Problem 16(choose chapter or problem)
The equation utt + cut + ku = a2 uxx + F(x, t), (i) where a2 > 0, c 0, and k 0 are constants, is known as the telegraph equation. It arises in the study of an elastic string under tension (see Appendix B of Chapter 10). Equation (i) also occurs in other applications. Assuming that F(x, t) = 0, let u(x, t) = X(x)T(t), separate the variables in Eq. (i), and derive ordinary differential equations for X and T.
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