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Unformatted text preview: at,le 0N MAP 2302 — Elementary Differential Equations — Fall 2011 November 21, 2011
Midterm 4 INSTRUCTIONS: This is a closed book exam and no notes are allowed. You are not to provide or
receive help from any outside source during the exam except that you may ask the instructor for
clariﬁcation of a problem. You have 50 minutes and you should attempt all problems. 0 Print your name in the space provided.
a Sign the FERPA release on the next page only if you wish your exam returned in lecture.
o CalculatOrs or other computing devices are not allowed. 0 Eccept when indicated, you must show all work and give a reason (or reasons) for your
answer. A correct answer with incorrect work will be considered wrong. 1. (25) Using power series techniques, ﬁnd a power series expansion at x = 0 for a general
solution to the djﬂerential equation y’2y=0. Your answer should be a power series, with an explicit formula for the coeﬁicients an.
.9 2. (10) Solve this differential equation in a different manner. Do your two solutions agree? Whyorwhynot?
l '/ 0‘ dx = 96x 3. (25) Find the ﬁrst four terms in a power series expansion at x = 0 for a general solution
to the differential equation
y’ + ysinz = e”. z 3 3700 +a,x +a2x “{3}< * 4. (25) Find the general solutiou to the differential equation 1:231” — 1571;3/ + 4y = 0. 5. (15) Find the singular points of the diﬁerential equation
2z(x — 2)2y” + 3my' + (a: — 2)y = 0
and classify each of them as regular or irregular.
//+ 3x /+__7,(:2/’7:Y_47:_O
7 ' ax(2<—2.)'wj ZXO‘
o a . I 2x0"
Cstvf‘j X Z:3/7<_/L ‘DNE ...
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