16. True or False: The equation y\' = x + y is separable. 17. True or False: The
ID: 2857440 • Letter: 1
Question
16. True or False: The equation y' = x + y is separable.
17. True or False: The function f(x) = ln(x)/x is a solution of the differential equation x^2y '+ xy = 1.
18. True or False: The differential equation y ' = x^2 sin(y) has infinitely many exceptional solutions.
19. True or False: All solutions to the differential equation y' = minus 1 minus y^4 are decreasing functions. 20.
True or False: The equation P(t) = Ce^kt where k < 0 models exponential growth.
21. True or False: The logistic differential equation is another model for population growth which reflects the fact that the relative growth rate decreases as the population increases, and becomes negative if the population grows beyond the maximum that the environment is capable of sustaining.
22. True or False: Using the model of the logistic differential equation, P' (t) = kP(1 minus P/K ), if the initial population is between 0 and K, then P'(t) > 0 and the population decreases.
23. True or False: The Monotone Convergence Theorem says that every increasing sequence converges.
Explanation / Answer
15- true
16- false
17-true
18- false
19- true
20- true
21- true
22- true
23- true
24 - true
25- false
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