[Solution Library] Suppose that a uniform metal rod 50 ~cm long is insulated laterally, and the temperatures at the exposed ends are maintained at 25^circ C and
Question: Suppose that a uniform metal rod \(50 \mathrm{~cm}\) long is insulated laterally, and the temperatures at the exposed ends are maintained at \(25^{\circ} \mathrm{C}\) and \(85^{\circ} \mathrm{C}\), respectively. Assume that an \(x\) axis is chosen as in the accompanying figure and that the temperature \(T(x)\) satisfies the equation
\[\frac{d^{2} T}{d x^{2}}=0\]Find \(T(x)\) for \(0 \leq x \leq 50\)
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