(a) Solve for x > 0, t > 0 (using the method of characteristics): c 0...

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(a) Solve for x > 0, t > 0 (using the method of characteristics): c² 0² u əx² ² u ди Ət Ət² u(x, 0) = f(x) (x, 0) = g(x) du (0, t) = 0, əx f(x) = {} = (Assume that u is continuous at x = 0, t = 0.) (b) Show that the solution of part (a) may be obtained by extending the initial position and velocity as even functions (around x = 0). (c) Sketch the solution if g(x) = 0 and {1 x > 0 t> 0. 4 < x < 5 otherwise. (a) Solve for x > 0, t > 0 (using the method of characteristics): c² 0² u əx² ² u ди Ət Ət² u(x, 0) = f(x) (x, 0) = g(x) du (0, t) = 0, əx f(x) = {} = (Assume that u is continuous at x = 0, t = 0.) (b) Show that the solution of part (a) may be obtained by extending the initial position and velocity as even functions (around x = 0). (c) Sketch the solution if g(x) = 0 and {1 x > 0 t> 0. 4 < x < 5 otherwise.