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ut = uxx
0 <x< 2, t> 0
u(x, 0) = x2 − x +1 0 ≤ x ≤ 2
u
(0, t)=1, u(2, t)=3
t > 0.
F

ut = uxx
0 <x< 2, t> 0
u(x, 0) = x^2 − x +1, 0 ≤ x ≤ 2
u(0, t)=1, u(2, t)=3, t > 0.

This problem explores solving the heat equation ut = uxx with boundary conditions u(0, t) = 1, u(2, t) = 3, and initial condition u(x, 0) = x^2 − x + 1 for 0 ≤ x ≤ 2. Learn about partial differential equations, boundary value problems, and separation of variables techniques, suitable for undergraduate students.

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