3. Let F and G be arbitrary differentiable functions of one variable.
Show that
u(x,t) = F(x+ct) + G(x-ct) is a solution to the wave equation
∂2u/∂t2 = c2(∂2u/∂x2), provided that F and G are sufficiently
smooth.
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PDEs and Burgers' equation are investigated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.