Change of variables

Hi everyone!

I'm currently stuck in the following question, any help is really appreciated.

Consider the equation

du/dt + du/dx = (d^2u/dx^2) + f(t,x) *

where d is the partial differential operator.
Using the change of variables (t,x) -> (s,y)=(t, x-t) show that * can be trasformed into an equation of the form

dU/ds = (d^2U/dy^2) + F(s,y)

where d is the partial differential operator, U(s,y)=u(s,y+s). Determine F(s,y).

Thanks

D.

Anyone?

Bump

What have you done so far?

Reply 4

Dialetheism

around

What have you done so far?

I haven't really done any significant step so far.
I've set s = t, y = x - t, ie x = y + s.
Then u(t,x) = u(s, y+s).
I've tried to use the differential form of the chain rule, but with no positive results.
I just don't get how am I supposed to do what I'm supposed to do.
Can you explain me how to use that change of variables to get the result?
Thank you very much!

D.