Problem 1E: Explain how to sketch the direction field of the equation y(t) = f(t, y), where f is given. Problem 2E Problem 3E Problem 4E Problem 5E: Direction fields A differential equation and its direction field are shown in the following figures.... Problem 6E Problem 7E Problem 8E: Identifying direction fields Which of the differential equations ad corresponds to the following... Problem 9E Problem 10E Problem 11E: Direction fields with technology Plot a direction field for the following differential equation with... Problem 12E: Sketching direction fields Use the window [2, 2] [2, 2] to sketch a direction field for the... Problem 13E: Sketching direction fields Use the window [2, 2] [2, 2] to sketch a direction field for the... Problem 14E: Sketching direction fields Use the window [2, 2] [2, 2] to sketch a direction field for the... Problem 15E: Sketching direction fields Use the window [2, 2] [2, 2] to sketch a direction field for the... Problem 16E: Sketching direction fields Use the window [2, 2] [2, 2] to sketch a direction field for the... Problem 17E: Increasing and decreasing solutions Consider the following differential equations. A detailed... Problem 18E: Increasing and decreasing solutions Consider the following differential equations. A detailed... Problem 19E: Increasing and decreasing solutions Consider the following differential equations. A detailed... Problem 20E: Increasing and decreasing solutions Consider the following differential equations. A detailed... Problem 21E: Logistic equations Consider the following logistic equations, for t 0. In each case, sketch the... Problem 22E: Logistic equations Consider the following logistic equations, for t 0. In each case, sketch the... Problem 23E: Logistic equations Consider the following logistic equations, for t 0. In each case, sketch the... Problem 24E: Logistic equations Consider the following logistic equations, for t 0. In each case, sketch the... Problem 25E: Two steps of Eulers method For the following initial value problems, compute the first two... Problem 26E: Two steps of Eulers method For the following initial value problems, compute the first two... Problem 27E: Two steps of Eulers method For the following initial value problems, compute the first two... Problem 28E: Two steps of Eulers method For the following initial value problems, compute the first two... Problem 29E: Errors in Eulers method Consider the following initial value problems. a.Find the approximations to... Problem 30E: Errors in Eulers method Consider the following initial value problems. a.Find the approximations to... Problem 31E Problem 32E Problem 33E Problem 34E Problem 35E Problem 36E Problem 37E Problem 38E: Equilibrium solutions A differential equation of the form y(t) = f(y) is said to be autonomous (the... Problem 39E Problem 40E Problem 41E: Equilibrium solutions A differential equation of the form y(t) = f(y) is said to be autonomous (the... Problem 42E Problem 43E: Equilibrium solutions A differential equation of the form y(t) = f(y) is said to be autonomous (the... Problem 44E: Direction field analysis Consider the first-order initial value problem y(t)=ay+b,y(0)=A, for t ... Problem 45E: Eulers method on more general grids Suppose the solution of the initial value problem... Problem 46E Problem 47E Problem 48E Problem 49E: Convergence of Eulers method Suppose Eulers method is applied to the initial value problem... Problem 50E: Stability of Eulers method Consider the initial value problem y'(t) = ay, y(0) = 1, where a 0; it... format_list_bulleted