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Supplementary Problems
Exercise 196.
(a) Solve the problem
u − u xx − 9u = 0 0 < x < π, t > 0,
t
4
u(0, t) = u (π, t) = 0 t ≥ 0,
x
u(x, 0) = sin(3x/2) + sin(9x/2) 0 ≤ x ≤ π.
(b) Compute ϕ(x): = lim u(x, t) for x ∈ [0, π].
t→∞
Exercise 197. Solve the problem
u = u xx − u, 0 < x < 1, t > 0,
t
u(0, t) = u (1, t) = 0 t ≥ 0,
x
u(x, 0) = x(2 − x) 0 ≤ x ≤ 1.
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