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= Question 5: (2 + 2 = 4 points, Challenge) a) (2 Points) Find the general solution of the partial differential equation: dular = duſat b) (2 Points) When solving the heat equation (see the Topic 6 video named ”The Heat Equation”) using the separation of variables method, reach a point where T'(t)/T(t) = X"(x)/x(x) = C and we used a negative constant (i.e., C = -12). Show that if we used a positive constant instead for C, for a rod of length l and assuming boundary conditions u(0,t) = 0) = u(l, t) that the only solution to the partial differential equation is u(x, t) = 0 for all x and all t.