99. Multiple Choice Which differential equation corresponds to the slope field below? dy (A) dx x In x 3 dy (B) = 12 - 1 dx dy (C) = In x dx dy In x -2 + (D) = dx -3384 Chapter 5 Differential Equations 5.2 Exercises See CalcChat.com for tutorial help and worked-out solutions to odd-numbered exercises. Solving a Differential Equation In Exercises 1-10, find the general solution of the Ly 18. differential equation. Writing and Solving a Differential Equation dy = 5 - 8x " dx In Exercises 19 and 20, write and find the general solution of the differential equation =y+3 4. y' = 6 - y that models the verbal statement. Evaluate the solution at the specified value of the 5. y' = 6. y' = independent variable. y' = Vxy 8. y' = x(1 + y) The rate of change of N is proportional to N. When (1 + x)y' - 2xy = 0 10. xy + y' = 100x 1 = 0, N = 250, and when ? = 1, N = 400. What is the value of N when t = 4? Writing and Solving a Differential Equation In 20. The rate of change of P is proportional to P. When Exercises 11 and 12, write and find the general solution 1 = 0, P = 5000, and when ? = 1, P = 4750. What is of the differential equation that models the verbal the value of P when t = 5? statement. 11. The rate of change of @ with respect to t is inversely Finding an Exponential Function In proportional to the square of t. Exercises 21-24, find the exponential function y = Cell that passes through the given points. 12. The rate of change of P with respect to f is proportional to 25 - 1. 22. Slope Field In Exercises 13 and 14, a (0. 4) differential equation, a point, and a slope field are given. (a) Sketch two approximate (4. 3) solutions of the differential equation on the (0. 2 slope field, one of which passes through the (5. -) given point. To print an enlarged copy of the graph, go to MathGraphs.com. (b) Use integration and the given point to find the 23. 24. particular solution of the differential equation (4.5) 4 and use a graphing utility to graph the solution. Compare the result with the sketch (1, 5) in part (a) that passes through the given point. 5, 2) 15 = x(6 - y). (0,0) 14. 2 =x (0. 4) (3. ) dx 25. Error Analysis Describe and correct the error when finding the particular solution of the differential equation y' = x/y where y(0) = 1. y dy = x- dx lydy = x dx Finding a Particular Solution In Exercises 15-18, find the function y = f() passing through the point (0, 10) with the given 72 = = +C differential equation. Use a graphing utility to graph the solution. HOP = (1 + C C= dy 16. dy = -951 1 213 - 342 =2 X