Chapter 6.5, Problem 35E

Mixture In Exercises 35-38, consider a tank that at time $t=0$ contains $v_0$ gallons of a solution of which, by weight, $q_0$ pounds is soluble concentrate. Another solution containing $q_1$, pounds of the concentrate per gallon is running into the tank at the rate of $r_1$, gallons per minute. The solulion in the tank is kept well stirred and is withdrawn at the rate of $r_2$, gallons per minute.

Let Q be the amount of concentrate (in pounds) in the solution at any time t. Show that

$\frac{dQ}{dt}+\frac{r_{2}Q}{v_0+(r_1-r_2)t}=q_1{r}_1$