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Unformatted text preview: MATH33B Exam 2 Name:
February 26, 2007 Section:
For full credit, show all work. 1 (12 points) For each of the following ordinary differential equations, determine its order,
whether or not the equation is linear, and whether the eqrration is homogeneous or inhomoge~ neous. _ 1
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(d) x2)?" + xy' + 2y = sinx f} ‘9‘ ‘53 !L‘é“ Em my." Q Show oﬁeo ft 9min 2 (10 points) Show that if the functions 311 and y; are lirrearly indepenrient solutions of y” +
p(x)y’ ~+ q(x)y m 0, then the two functions y; +312 and y1 — yg also form a fundamental set of
solutions. 5.5% mng it)
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Xvi z 2 x Mm an a Am Q Viz XWE; 33;; 3%“: ﬂag m 4 (26 points) Given that (1 +x) and 8" are solutions of the homogeneous equation corresponding
to xy" m (1 +x)y’ + y m x263, x > 0, ﬁnd a particular solution of the differential equation. X.
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36 3%.? 0%“ 22"" 5 {26 points) With no damping, a spiral spring is stretched .98 m by a mass that weighs 1 kg. The
damping constant ,u = 7kg/s. If the mass is subjected to an external fqree of the form 4:105 2:,
ﬁnd and identify the transient and steady state response of the system. How many times does the
solution cross the time axis as t a 00? .. WW 3 v z . NE
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This note was uploaded on 04/02/2008 for the course MATH 33B taught by Professor Staff during the Winter '07 term at UCLA.
 Winter '07
 staff
 Math

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