Solve the heat flow problem Ju t dr = 3- = (0,t)...
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Solve the heat flow problem ди J²u Ət dr² ди дг ди = 3- = (0,t) = 0. (π, t) = 0, дх u(x,0) = 2- cos 2x + 5 cos 3x, ди ²u Ət 0x²¹ u(0, t) = 0, u(1, t) = 1, u(x,0) = x², t> 0, 0<x<T, [In this problem and the following ones, it is not necessary to repeat the separation of variables: you may use the appropriate formal solution of the PDE and boundary conditions found in notes and lectures.] 2. (10 points) Solve the heat flow problem t> 0, t> 0, 0 ≤x≤T. t> 0, 0<x< 1, t> 0. t> 0, 0≤x≤ 1. Solve the heat flow problem ди J²u Ət dr² ди дг ди = 3- = (0,t) = 0. (π, t) = 0, дх u(x,0) = 2- cos 2x + 5 cos 3x, ди ²u Ət 0x²¹ u(0, t) = 0, u(1, t) = 1, u(x,0) = x², t> 0, 0<x<T, [In this problem and the following ones, it is not necessary to repeat the separation of variables: you may use the appropriate formal solution of the PDE and boundary conditions found in notes and lectures.] 2. (10 points) Solve the heat flow problem t> 0, t> 0, 0 ≤x≤T. t> 0, 0<x< 1, t> 0. t> 0, 0≤x≤ 1.
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