4. Consider the heat equation with a negative source:
ut = - 6x, 0 ＜ x ＜ 1, t ＞ 0
u(0, t) = u(1, t) = 0
u(x, 0) = u0, 0 ＜ x ＜ 1
where u0 ＞ 0 is a constant
(a)Find the steady-state solution
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- 6x, 0 ＜ x ＜ 1, t ＞ 0