Let u be the solution to the initial boundary value problem for the Heat Equation, au(t,...

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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, ²1), € [2³/1). € [2/1.3]. 0, XE The solution u of the problem above, with the conventions given in class, has the form u(t, x) = C₁ U₂(t) w₁(x), x==1 with the normalization conditions v₂ (0) = 1, W₂ (2) = 1. U Find the functions U, W. and the constants c Un (1) = w₁(x) = Cn ܐ- M M Σ 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, ²1), € [2³/1). € [2/1.3]. 0, XE The solution u of the problem above, with the conventions given in class, has the form u(t, x) = C₁ U₂(t) w₁(x), x==1 with the normalization conditions v₂ (0) = 1, W₂ (2) = 1. U Find the functions U, W. and the constants c Un (1) = w₁(x) = Cn ܐ- M M Σ

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