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Question: the problem is that i dont know if uwxtvx or...

Question details

The problem is that I don't know if u=w(x,t)+v(x) or u=XT in the PDE. I know that I have to judge from the conditions given. But I still don't understand.

For example:

(1.)alpha^{2}v_{xx}=v_{t}+hv,(0<x<L,0<t<infty );v(0,t)=v(L,t)=100,v(x,o)=F(x)

The answer let the ta,tb .

(2.)alpha ^{2} heta _{xx}= heta _{tt}, heta (x,t)=kx, heta _{t}(x,0)=0, heta _{x}(L,t)=0

The answer use the separation of variables,directly, U=XT.

Please leave the detail and the reason, thanks!

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