We wish to solve the PDE

u_{tt} = 9 u_{xx} , \qquad -\infty < x < \infty , \quad t > 0

Guess solutions of the formu = e^{\alpha x+\beta t} (find a relationship between
\alpha and \beta ).

Suppose you knowu(x,0) = e^{x} . There are exactly two solutions of the above
form, one with a positive u_t(x,0) and one with negative u_t(x,0) .
The first is:

u = {}

And the second is

u = {}

help (formulas)

Guess solutions of the form

Suppose you know

And the second is

help (formulas)

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