Ononot — An object cools according to Newton's law: \frac{dT}{dt} = -

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Differential Equationshard

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An object cools according to Newton's law: $\frac{dT}{dt} = -k(T - T_s)$ . If the initial temperature is $T_0$ and the ambient temperature $T_s$ is increasing linearly with time, $T_s(t) = T_s(0) + \alpha t$ , what is the form of the solution?