A How to separate variables in this PDE?

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Can anyone suggest a way to separate the variables in this PDE, so I can solve it analytically?
My PDE:
F,x,t + A(x)*F(x,t)*[(x+t)^(-3/2)] = 0

A(x) is a known function of x.
Trying to separate F(x,t) like
F(x,t) = F1(x)*F2(t)*F3(x+t).

I’m getting desperate to solve,
any suggestions??
 
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Make the change of variable (\zeta, \eta) = (x, x + t). Then the Ansatz F = H(\eta)Z(\zeta) yields <br /> H&#039;(\eta)Z&#039;(\zeta) + H&#039;&#039;(\eta)Z(\zeta) + A(\zeta)H(\eta)Z(\zeta)\eta^{-3/2} = 0. I'm not sure this is separable.
 
Thanks pasmith,
I did try something like that, and basically got that same type of equation, but I’m not sure what to do with it next. Still searching…
 
It wwould surely be easier to parse in ##LaTeX##
 
F_{,x,t} + \frac{A(x)}{(x+t)^{3/2}} F(x,t) = 0

A(x) is messy but known; F(x,t) must be solved for analytically, through separability or any other way.
 
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What is ##F_{,x,t} ##?
 
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Common notation, F_{,x,t} \equiv \frac{\partial ^{2} F(x,t)}{\partial x \partial t}
 
Wow I've never seen it with the commas. OK thanks.
 
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