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Suppose u(t,x) and v(t,x ) is C^2 functions defined on R^2 that satisfy the first-order system...

Suppose u(t,x) and v(t,x ) is C^2 functions defined on R^2 that satisfy the first-order system of PDE Ut=Vx, Vt=Ux,

A.) Show that both U and V are classical solutions to the wave equations  Utt= Uxx.

Which result from multivariable calculus do you need to justify the conclusion.

B)Given a classical sol. u(t,x) to the wave equation, can you construct a function v(t,x) such that u(t,x), v(t,x)

form of sol. to the first order system.

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