In Prob. 16, vary the initial conditions systematically, describe and explain the graphs physically. The great variety of curves will surprise you. Are they always periodic? Can you find empirical laws for the changes in terms of continuous changes of those conditions?

Data from Prob. 16

y'₁ + y'₂ = 2 sinh t, y'₂ + y'₃ = e^t, y'₃ + y'₁ = 2e^t + e^-t, y₁(0) = 1, y₂(0) = 1, y₃(0) = 0