... < x < ∞, t > 0,u(x, 0) = f (x), ut(x, 0) = g(x) −∞ < x < ∞,wheref (x) =x 0 < x < 1,11< x < 2,3 − x 2 < x < 3,0 x > 3, x < 0,g(x) =1 ... the domain {(x, t) |−∞< x < ∞, t > 0}.4.16 Solve the problemutt− uxx= xt −∞ < x < ∞, t > 0,u(x, 0) = 0 −∞ < x < ∞,ut(x, 0) = ex−∞ < x < ∞.4.17 (a) Without ... 00< x < ∞, t > 0,u(0, t) = t2t > 0,u(x, 0) = x20 ≤ x < ∞,ut(x, 0) = 6x 0 ≤ x < ∞,and evaluate u(4, 1) and u(1, 4).4.3 Consider the problemutt− 4uxx= 0 −∞ <...