MATH 240 Midterm: MATH 240 KSU Test 1f06
15 Feb 2019
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Show all your work in the space under each question. Please write legibly and organize your solutions in a logical and coherent form; answers which are illegible or confusing will not receive credit. Each problem is worth 10 points: find the general solution. y2 + 1 xy dy dx. = 0: find the general solution. dy dx. (tan x)y = 1: find the general solution. dy dx. P (0) = 1: a population is described by the equation dp dt. = p (p 1)(p 7). (2 pts. ) (a) find the critical points of this equation. (4 pts. ) (b) determine the intervals on which p is increasing and decreasing. Draw a graph of p with several di erent initial values. Your graph must be well drawn and readable. (4 pts. ) (c) determine if each critical point you found in (a) is stable or unstable.
