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**Unformatted text preview: **Math 415.01 — Quiz 4 - 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 : k0. . I (1) (17 pts) Find the solution of the given initial value problem. Sketch a rough graph of
the solution indicating long term behavior. 3/” + 331’ — 4y = 0, 9(0) = 3, y’(0) = -7 (2) (8 pts) Suppose ¢(t) is a solution to y" + p(t)y’ + (1(t)y = 90) Show that
(a) If c is any nonzero constant and g(t) = 0, then c¢(t) is also a solution. (b) If d is any nonzero constant and g(t) is not always zero, then d¢(t) is not a
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MI 1 M4 M +93% ; 4w m «as» Math 415.01 - Quiz 4 — 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. namemumber : ° l (1) (7 pts) Determine the longest interval where a unique twice dlﬁerentiable solution exists
for the given initial value problem (t — 3)y” + (t - 2)y’ + (t — 3)y = sec(x) I Cm);0, yC~)>o (2) (18 pts) Find the solution of the initial value prob em 2y” - 3y’ + y = 0, 21(0) = 2, y'(0) = MIn—t and thereby ﬁnd (a) Find the maximum value of the solution (b) Find where the solution is zero. ...

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