Hot water at a constant volumetric flow rate of $F_h$ and temperature $T_h(t)$ is mixed with cold water at a constant volumetric flow rate of $F_c$ and a constant temperature of $T_c.$ Both streams flow into a bathtub, but because of carelessness, the water is overflowing and keeping the bathtub full of water. The bathtub volume is $V,$ and the heat loss can be ignored. Assuming the water in the bathtub is perfectly mixed and constant density and heat capacity, derive the differential equation relating the temperature in the bathtub, $T(t),$ to the temperature of the hot water, $T_h(t).$