Initially, two large tanks A and B each hold 100 gallons of brine. The well-stirred liqu...

Initially, two large tanks A and B each hold 100 gallons of brine. The well-stirred liquid is pumped between the tanks as shown in Figure 3.R.3. Use the information given in the figure to construct a mathematical model for the number of pounds of salt x₁(t) and x₂(t) at time t in tanks A and B, respectively.

When all the curves in a family G(x, y, c₁) = 0 intersect orthogonally all the curves in another family H(x, y, c₂) = 0, the families are said to be orthogonal trajectories of each other. See Figure 3.R.4. If dy/dx = f (x, y) is the differential equation of one family, then the differential equation for the orthogonal trajectories of this family is