Suppose a container has 46 of saltwater with a salt concentration of 0.25 kg/L. Further suppose that brine with a Salt concentration of 0.5kg/2 is pumped into the container at 3 1 / min and pumped out at a rate of 21 / min. Let y( t) be the amount in Kilograms of salt in the container wher t is in minutes. ( a) show that the amount of salt in the container satisfies the differential equation dy. 3 It = 2 4 + + + y (o ) = 1 ( b) Solve the initial value problem and find the amount of time it takes for there to be 1.5 kg of salt in the container.d An autonomous differential equation is of the form dy 2 y) Here, the independent variable, :3, is missing a: from the right hand side of the equation. When the independent variable is time, denoted by t, these differential d equations of the form 011: = f (y) are called time-invariant differential equations. Note that if f (c) = 0, then y = c Will be a solution to the autonomous di'erential equation. The value c is called a steady state or an equilibrium solution. We can nd the steady state by setting the derivative in the differential equation to zero