define [tex] L = a \frac{\partial^2u}{\partial t^2} + B \frac{\partial^2 u}{\partial x \partial t} + C \frac{\partial^2u}{\partial x^2} = 0 [/tex](adsbygoogle = window.adsbygoogle || []).push({});

show that if L is hyperbolic then and A is not zero the transofmartion to moving coordinates

[tex] x' = x - \frac{B}{2A} t [/tex]

[tex] t' = t [/tex]

tkaes L into a multiple of the wave operator

now how would igo about changing the variables in L to x' and t'?

i mean i could certainly find out

[tex] \frac{\partial x}{\partial u} [/tex] amd [tex] \frac{\partial t'}{\partial u} [/tex] and use this identitity that

[tex] \frac{\partial u}{\partial x} = \frac{1}{\frac{\partial x}{\partial u}} [/tex]

but im not sure how to proceed from there

please help

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# Change of variables

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