Question: Show that the heat equation u t = c 2 u xx , 0 x L, can be transformed

Show that the heat equation u^∼_t_∼ = c²u^∼_xx, 0 ≤ x^∼ ≤ L, can be transformed to the “nondimensional” standard form u_t = u_xx, 0 ≤ x ≤ 1, by setting x = x^∼/L, t = c²t^∼/L², u = u^∼/u₀, where u₀is any constant temperature.

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