Let k be a positive constant. Let 1 2 Tkt - e-(2-4) /4kt f() dE, u(x,...

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Let k be a positive constant. Let 1 2√ Tkt - e-(2-4)² /4kt f(£) dE, u(x, t) = in which f is continuous on the real line. Show that ut = kurr for -∞< x <∞, t > 0. Also determine u(x, t) when f(x) = 1 for all real x. Hint: Use a change of variables and the standard result that Le-w dw = √. Let k be a positive constant. Let 1 2√ Tkt - e-(2-4)² /4kt f(£) dE, u(x, t) = in which f is continuous on the real line. Show that ut = kurr for -∞< x <∞, t > 0. Also determine u(x, t) when f(x) = 1 for all real x. Hint: Use a change of variables and the standard result that Le-w dw = √.