Exercise 3.1.4 A population is modeled by the differential equation dP P = = 1.2P dt 4200 (a) For what values of P is the population increasing? (b) For what values of P is the population decreasing? (c) What are the equilibrium solutions? Exercise 3.1.5 A function y(t) satisfies the differential equation dy - = y 6y +5y dt (a) What are the constant solutions? (b) For what values of y is y increasing? (c) For what values of y is y decreasing? Exercise 3.1.6 k k Show that x(t) = a sin + cos t is a solution to m m dx dt m