Consider two large mixing tanks shown in the figure below. Suppose tanks A initially contains 80 gallons of liquid and tank B initially contains 50 gallons of liquid. A liquid with a salt concentration of 3 lbs/gal is pumped into tank A. The well-stirred liquid is pumped in and out of the tanks as shown in the figure. Construct a system of first-order differential equations for the number of pounds of salt, x(t) and y(t), in tanks A and B at time t, respectively. Do not solve the system. Express your solution in the matrix/vector form X'(t) = AX(t) + F(t). How many pounds of salt will eventually be in tank B? %3D

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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.