Repeat Problem 4 for the case when the temperature of the water tank increases linearly with time at a rate of \(r\).

Data From Problem 4:

The temperature of a steel sphere with initial temperature \(T_{0}\) submerged in water with temperature \(T_{i}\) is governed by the initial-value problem \[R C \dot{T}+T=T_{i}, \quad T(0)=T_{0}\]
where:
\(R\) is the thermal resistance due to convection \(C\) is the thermal capacitance of the sphere