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(a) Separate the following partial differential equation into two ordinary differential equations: Utt + 4Utx −...

(a) Separate the following partial differential equation into two ordinary differential equations: Utt + 4Utx − 2U = 0. (b) Given the boundary values U(0,t) = 0 and Ux (L,t) = 0, L > 0, for all t, write an eigenvalue problem in terms of X(x) that the equation in (a) must satisfy.

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