Problem 1RCC: (a) What is a differential equation? (b) What is the order of a differential equation? (c) What is... Problem 2RCC: What can you say about the solutions of the equation y' = x2 + y2 just by looking at the... Problem 3RCC: What is a direction field for the differential equation y' = F(x, y)? Problem 4RCC: Explain how Euler's method works. Problem 5RCC: What is a separable differential equation? How do you solve it? Problem 6RCC: What is a first-order linear differential equation? How do you solve it? Problem 7RCC: (a) Write a differential equation that expresses the law of natural growth. What does it say in... Problem 8RCC: (a) Write the logistic differential equation. (b) Under what circumstances is this an appropriate... Problem 9RCC: (a) Write Lotka-Volterra equations to model populations of food-fish (F) and sharks (S). (b) What do... Problem 1RQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,... Problem 2RQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,... Problem 3RQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,... Problem 4RQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,... Problem 5RQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,... Problem 6RQ Problem 7RQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,... Problem 1RE: (a) A direction field for the differential equation y' = y(y 2)(y 4) is shown. Sketch the graphs... Problem 2RE: (a) Sketch a direction field for the differential equation y' = x/y. Then use it to sketch the four... Problem 3RE: (a) A direction field for the differential equation y' = x2 y2 is shown. Sketch the solution of the... Problem 4RE: (a) Use Euler's method with step size 0.2 to estimate y(0.4), where y(x) is the solution of the... Problem 5RE: Solve the differential equation. 5. y=xesinxycosx Problem 6RE: Solve the differential equation. 6. dxdy=1t+xtx Problem 7RE: Solve the differential equation. 7. 2yey2y=2x+3x Problem 8RE: Solve the differential equation. 8. x2yy=2x3e1/x Problem 9RE: Solve the initial-value problem. 9. drdt+2tr=r,r(0)=5 Problem 10RE: Solve the initial-value problem. 10. (1 + cos x) y' = (1 + ey) sin x, y(0) = 0 Problem 11RE: Solve the initial-value problem. 11. xy' y = x ln x, y(1) = 2 Problem 12RE: Solve the initial-value problem y' = 3x2ey, y(0) = 1 , and graph the solution. Problem 13RE: Find the orthogonal trajectories of the family of curves. 13. y = kex Problem 14RE: Find the orthogonal trajectories of the family of curves. 14. y = ekx Problem 15RE: (a) Write the solution of the initial-value problem dPdt=0.1P(1P2000)P(0)=100 and use it to find the... Problem 16RE: (a) The population of the world was 6.1 billion in 2000 and 6.9 billion in 2010. Find an exponential... Problem 17RE: The von Bertalanffy growth model is used to predict the length L(t) of a fish over a period of time.... Problem 18RE: A tank contains 100 L of pure water. Brine that contains 0.1 kg of salt per liter enters the tank at... Problem 19RE: One model for the spread of an epidemic is that the rate of spread is jointly proportional to the... Problem 20RE: The Brentano-Stevens Law in psychology models the way that a subject reacts to a stimulus. It states... Problem 21RE: The transport of a substance across a capillary wall in lung physiology has been modeled by the... Problem 22RE: Populations of birds and insects are modeled by the equations dxdt=0.4x0.002xydydt=0.2y+0.000008xy... Problem 23RE: Suppose the model of Exercise 22 is replaced by the equations... Problem 24RE: Barbara weighs 60 kg and is on a diet of 1600 calories per day, of which 850 are used automatically... Problem 1P: Find all functions f such that f' is continuous and [f(x)]2=100+0x{[f(t)2]+[f(t)2]}dtforallreadx Problem 2P: A student forgot the Product Rule for differentiation and made the mistake of thinking that (fg)' =... Problem 3P: Let f be a function with the property that f(0) = 1, f'(0) = 1, and f(a + b) = f(a) f(b) for all... Problem 4P: Find all functions f that satisfy the equation (f(x)dx)(1f(x)dx)=1 Problem 5P: Find the curve y = f(x) such that f(x) 0, f(0) = 0, f(1) = 1, and the area under the graph of f... Problem 6P: A subtangent is a portion of the x-axis that lies directly beneath the segment of a tangent line... Problem 7P: A peach pie is taken out of the oven at 5:00 pm. At that time it is piping hot, 100C. At 5:10 pm its... Problem 8P: Snow began to fall during the morning of February 2 and continued steadily into the afternoon. At... Problem 9P: A dog sees a rabbit running in a straight line across an open field and gives chase. In a... Problem 10P: (a) Suppose that the dog in Problem 9 runs twice as fast as the rabbit. Find a differential equation... Problem 11P: A planning engineer for a new alum plant must present some estimates to his company regarding the... Problem 12P: Find the curve that passes through the point (3, 2) and has the properly that if the tangent line is... Problem 13P: Recall that the normal line to a curve at a point P on the curve is the line that passes through P... Problem 14P: Find all curves with the properly that if the normal line is drawn at any point P on the curve, then... Problem 15P: Find all curves with the property that if a line is drawn from the origin to any point (x, y) on the... format_list_bulleted