Water flows into a tank at the variable rate of Rin = 20/(1 + t)gal/min and out at the constant rate Rout = 5 gal/min. Let V (t) be the volume of water in the tank at time t . (a) Set up a differential equation for V (t) and solve it with the initial condition V (0) = 100. (b) Find the maximum value of V . (c) Plot V (t) and estimate the time t when the tank is empty.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.