questions are below:

Draw the isoclines with their direction markers and sketch several solution curves, including the curve satisfying the given initial condition. Choose the correct sketch below. OC. OA. Draw the isoclines with their direction markers and sketch several solution curves, including the curve satisfying the given initial condition. dy dx -= 5x + 3y, y(0) = 2 Choose the correct sketch below. O A. O B. Ay O c. . N' 1 . 1 . . .6 6 X 1 1. 4. 1 . .F 6 1 1. . 1 .Consider the differential equation - = -p(p - 1.5)(p - 3) for the population p (in thousands) of a certain species at time t. Complete parts (a) through (e) below. (a) Sketch the direction field by using either a computer software package or the method of isoclines. Choose the correct sketch below. O A. O B. O c. AP Ap (b) If the initial population is 3300 [that is, p(0) = 3.3], what can be said about the limiting population lim p(t)? t-+ + 00 If p(0) = 3.3, then lim p(t) = . The population will 1 - + 00 (c) If p(0) = 2.5, what can be said about the limiting population lim p(t)? 1-+ + 00 If p(0) = 2.5, then lim p(t) = . The population will 1-+ 00(d) If p(0)= 1.3, what can be said about the limiting population lim p(t)? t> + on If p(O) = 13, then lim p(t) = . The population will 1 t> + co (e) Can a population of 2300 ever decline to 600? ? it V possible for a population of 2300 to decline to 600. One solution of the given differential equation is the horizontal line p(t) = . If the population were to decline from 2300 to 600, the corresponding solution curve would V that horizontal line. This would i: what is guaranteed by the existence-uniqueness theorem