Question: Let u be the solution to the initial boundary value problem for the Heat Equation, au(t, x) = 2u(t, x), 1 (0,00), x (0,3);

Let u be the solution to the initial boundary value problem for the Heat Equation, du(t, x) = 2 ult, x), te (0,0), X? (0,3);

Let u be the solution to the initial boundary value problem for the Heat Equation, au(t, x) = 2u(t, x), 1 (0,00), x (0,3); with boundary conditions u(t,0)= 0, u(t, 3) = 0, and with initial condition 0, XE r3 u(0, x) = f(x) = 5, x [0, 1), [2/1). [2/1.3]. 0, XE The solution u of the problem above, with the conventions given in class, has the form u(t, x) = C U(t) w(x), x==1 with the normalization conditions v (0) = 1, W (2) = 1. U Find the functions U, W. and the constants c Un (1) = w(x) = Cn - M M

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