Question: Separate the following partial differential equation into two ordinary differential equations 2. (a) Separate the following partial differential equation into two ordinary differential equations: tx

Separate the following partial differential equation into two ordinary differential equations

2. (a) Separate the following partial differential equation into two ordinary differential equations: tx Ux + 6tx Uxt - 7txe3x Un = 0. (b) Given the boundary values Ux(0,t) = 0 and U(n,t) = 0, for all t, write an eigenvalue problem in terms of X(x) that the equation of X found in (a) must satisfy. (That is, state the resulting eigenvalue problem that you would solve next, only. You do not need to actually solve it. Likewise for 3(b) below.)

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