2302f11-mid4-soln - at,le 0N MAP 2302 — Elementary...

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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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2302f11-mid4-soln - at,le 0N MAP 2302 — Elementary...

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