C1*Ux+C2*Ut+C1*C2*Uxt=0, C1 and C2 are constant

[p.sarafraz]

Hello every one. I'm doing research related to heat transfer stuff. I came up with this PDE after making some assumptions on my model. Now I need to solve it to be able to describe my model in a simple way. U is only a function of x and t.

C1*Ux+C2*Ut+C1*C2*Uxt=0, C1 and C2 are constant!

Thanks in advance.

 

[haruspex]

The system is homogeneous, so assume any solution can be expressed as a sum of products of functions of x and t separately. Substitute U = f(x).g(t) to find the set of such products.

 

[p.sarafraz]

Thans for your reply. I tried this technique but it appears that f function depends on g and g depends on f. And I don't know what I can do with that.

 

[haruspex]

Thans for your reply. I tried this technique but it appears that f function depends on g and g depends on f. And I don't know what I can do with that.

If you can get it into the form (some function of f, f', x) = (some function of g, g', t), which I believe you can, then you can conclude that both sides of that equal a constant, C. Do you see why?

 

[p.sarafraz]

Oh yes I understand. Thank you so much. This is a great help.