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- Homework Statement
- Find the transformed solution to the 2nd order PDE uxx + uxt + utt = 0

- Relevant Equations
- Fourier transform equation

I just want to make sure I am on the right track here (hence have not given the other information in the question). In taking the Fourier transform of the PDE above, I get:

F{uxx} = iω^2*F{u},

F{uxt} = d/dt F{ux} = iω d/dt F{u}

F{utt} = d^2/dt^2 F{u}

Together the transformed PDE gives a second order ODE which is: iω^2*F{u} + iω d/dt F{u} + d^2/dt^2 F{u} = 0.

Are these transformations correct??

Thanks!

F{uxx} = iω^2*F{u},

F{uxt} = d/dt F{ux} = iω d/dt F{u}

F{utt} = d^2/dt^2 F{u}

Together the transformed PDE gives a second order ODE which is: iω^2*F{u} + iω d/dt F{u} + d^2/dt^2 F{u} = 0.

Are these transformations correct??

Thanks!