Text: do a, b, and c. Thanks! I got the others. Oux, t Oux, t, xER ax^2 Subject to the initial condition u(x,0) = 0. a) 8 points Show that u(x,t) = sin(cat*sin(g)) is the solution of the initial value problem. b) 12 points Prove or disprove that the initial value problem is unique. c) 6 points Use a trigonometric identity to rewrite the solution as the average of two traveling wave solutions w((x-ct)). d) 5 points Use Matlab to plot the surface solution u(x,t) for 0 < x < 20, 0 < t < 20, a = ? and c = 2. e) 5 points Use Matlab to plot the wave solutions for t = 5 and 0 < x < 20. f) 4 points What is the connection between the plots in parts (d) and (e)?

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