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(a) Separate the following partial differential equation into two ordinary differential equations: e 5t t 6...

(a) Separate the following partial differential equation into two ordinary differential equations: e 5t t 6 Uxx + 7t 2 Uxt − 6t 2 Ut = 0. (b) Given the boundary values Ux (0,t) = 0 and U(2π,t) = 0, for all t, write an eigenvalue problem in terms of X(x) that the equation in (a) must satisfy. That is, state (ONLY) the resulting eigenvalue problem that you would need to solve next. You do not need to actually solve it. Same for 5(b) below.

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