Answer to Question #40210 in Differential Equations for nate ruiz

Question

PLEASE ANSWER THIS; I have used this site many times in the past, but in recent months the only answer I get is that my question is too involved for a free answer; I don't know if you have just been getting cheap or lazy, but I could use expert help here. Thanks.

PDE: Initial Value Problem.

U_tt - c^2U_xx = 0 x in R, t greater than or equal to 0, c = 1.
U(x,0) = #(x)
U_t(x,0) = 0

Define #(x) = 1 if (abs. value)x less than or equal to 1, 0 if (abs. value)x greater than 1.

Find formula for the solution u(x,t) for any x in R, t greater than or equal to 0.
Sketch the graph of u(x,t) as a function of x for t = 0, t = 1/2, t = 1, t = 2.
Explain why the area under the graph dfoes not change with it.