Problem 1E: In Problems 1 and 2, y = 1/(1 + c1ex) is a one-parameter family of solutions of the first-order DE y... Problem 2E: In Problems 1 and 2, y = 1/(1 + c1ex) is a one-parameter family of solutions of the first-order DE y... Problem 3E: In Problems 36, y = 1/(x2 + c) is a one-parameter family of solutions of the first-order DE y + 2xy2... Problem 4E: In Problems 36, y = 1/(x2 + c) is a one-parameter family of solutions of the first-order DE y + 2xy2... Problem 5E: In Problems 36, y = 1/(x2 + c) is a one-parameter family of solutions of the first-order DE y + 2xy2... Problem 6E: In Problems 36, y = 1/(x2 + c) is a one-parameter family of solutions of the first-order DE y + 2xy2... Problem 7E: In Problems 710, x = c1 cos t + c2 sin t is a two-parameter family of solutions of the second-order... Problem 8E Problem 9E: In Problems 710, x = c1 cos t + c2 sin t is a two-parameter family of solutions of the second-order... Problem 10E: In Problems 710, x = c1 cos t + c2 sin t is a two-parameter family of solutions of the second-order... Problem 11E: In Problems 1114, y = c1ex + c2ex is a two-parameter family of solutions of the second-order DE y y... Problem 12E: In Problems 1114, y = c1ex + c2ex is a two-parameter family of solutions of the second-order DE y y... Problem 13E: In Problems 1114, y = c1ex + c2ex is a two-parameter family of solutions of the second-order DE y y... Problem 14E: In Problems 1114, y = c1ex + c2ex is a two-parameter family of solutions of the second-order DE y y... Problem 15E: In Problems 15 and 16 determine by inspection at least two solutions of the given first-order IVP.... Problem 16E: In Problems 15 and 16 determine by inspection at least two solutions of the given first-order IVP.... Problem 17E: In Problems 1724 determine a region of the xy-plane for which the given differential equation would... Problem 18E: In Problems 1724 determine a region of the xy-plane for which the given differential equation would... Problem 19E: In Problems 1724 determine a region of the xy-plane for which the given differential equation would... Problem 20E: In Problems 1724 determine a region of the xy-plane for which the given differential equation would... Problem 21E: In Problems 1724 determine a region of the xy-plane for which the given differential equation would... Problem 22E: In Problems 1724 determine a region of the xy-plane for which the given differential equation would... Problem 23E: In Problems 1724 determine a region of the xy-plane for which the given differential equation would... Problem 24E: In Problems 1724 determine a region of the xy-plane for which the given differential equation would... Problem 25E: In Problems 2528 determine whether Theorem 1.2.1 guarantees that the differential equation y=y29... Problem 26E: In Problems 2528 determine whether Theorem 1.2.1 guarantees that the differential equation y=y29... Problem 27E: In Problems 2528 determine whether Theorem 1.2.1 guarantees that the differential equation y=y29... Problem 28E: In Problems 2528 determine whether Theorem 1.2.1 guarantees that the differential equation y=y29... Problem 29E: (a) By inspection find a one-parameter family of solutions of the differential equation xy = y.... Problem 30E: (a) Verify that y = tan (x + c) is a one-parameter family of solutions of the differential equation... Problem 31E: (a) Verify that y = 1 /(x + c) is a one-parameter family of solutions of the differential equation... Problem 32E: (a) Show that a solution from the family in part (a) of Problem 31 that satisfies y = y2, y(1) = 1,... Problem 33E: (a) Verify that 3x2 y2 = c is a one-parameter family of solutions of the differential equation y... Problem 34E: (a) Use the family of solutions in part (a) of Problem 33 to find an implicit solution of the... Problem 35E: In Problems 3538 the graph of a member of a family of solutions of a second-order differential... Problem 36E: In Problems 3538 the graph of a member of a family of solutions of a second-order differential... Problem 37E: In Problems 3538 the graph of a member of a family of solutions of a second-order differential... Problem 38E: In Problems 3538 the graph of a member of a family of solutions of a second-order differential... Problem 39E: In Problems 3944, y = c1 cos 2x + c2 sin 2x is a two-parameter family of solutions of the... Problem 40E: In Problems 3944, y = c1 cos 2x + c2 sin 2x is a two-parameter family of solutions of the... Problem 41E: In Problems 3944, y = c1 cos 2x + c2 sin 2x is a two-parameter family of solutions of the... Problem 42E: In Problems 3944, y = c1 cos 2x + c2 sin 2x is a two-parameter family of solutions of the... Problem 43E: In Problems 3944, y = c1 cos 2x + c2 sin 2x is a two-parameter family of solutions of the... Problem 44E: In Problems 3944, y = c1 cos 2x + c2 sin 2x is a two-parameter family of solutions of the... Problem 45E: Find a function whose graph at each point (x, y) has the slope given by 8e2x + 6x and has the... Problem 46E Problem 47E: Consider the initial-value problem y = x 2y, y(0) = 12. Determine which of the two curves shown in... Problem 48E: Show that x=0y1t3+1dt is an implicit solution of the initial-value problem 2d2ydx23y2=0, y(0) = 0,... Problem 49E Problem 50E: Suppose that the first-order differential equation dy/dx = f(x, y) possesses a one-parameter family... Problem 51E: The functions y(x)=116x4, x and y(x)={0,x0116x4,x0 have the same domain but are clearly... format_list_bulleted