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**Unformatted text preview: **Math 415.01 — Quiz 3 — 10:30 recitation (Vutha) The following quiz is worth 25 points. You have 20 minutes to attempt it. Please show
all work. Answers without work will receive no credit. You may use both sides of the paper. namemumber : o I (1) (12 pts) Sketch a graph of f (y) versus y for the given differential equation. Draw the
phase line and sketch several solutions. Also find all equilibria and their stability. (2) (13 pts) Find the value of b that makes the following equation exact, and solve the
equation. (2:312 + bxy)da: + 2:2(y + 2)dy = 0 f0!) Math 415.01 - Quiz 3 - 11:30 recitation (Vutha) The following quiz is worth 25 points. You have 20 minutes to attempt it. Please show
all work. Answers without work will receive no credit. You may use both sides of the paper. name.number : V (A 'H.\C3L o I
4+0, real» cal-4M
(1) (13 pts) Is the following equation exact ‘? If yes, ﬁnd; so ution.-H~ak, on y . (yew cos(2a:) — 2e” sin(2m) + 2:5)d2: + (xe’y cos(3m) — 3)dy = 0 (2) (12 pts) Find all equilibria and stability for the given equation. Also draw a phase line
and sketch a few solutions. %=ay2—by, a>0, b>0,y020 O Vl: yexllooscbc) ‘ ZQXYSMZX + 1X
N ‘— xefyCOSCZX) :3 M7 = 7 (ﬂex) Cos (2x) + eI‘Y. CosClx)
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