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exam1W09sol - Name-Section/Time of lecture-Professor/GSI...

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Name: -------------------------------- Section/Time of lecture: -------------------------------- Professor/GSI: ______________ _ MATH 216 WINTER 2009 MIDTERM I To get full score you need to carefully explain what you did. No calculators allowed. 1
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I Problem I Points I Score I 1 10 2 28 3 22 4 26 2 I TOTAL I 88 2
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Problem 1. I a-4 pt I Verify that the function y ( x) = x 2 sin x satisfies y" - y' + y = 3x cos x. X 2 ' y 5M1 X \j ~ 2x~~-r Y:~X !I 2_ ~ _ 2 ~·'I )( -+- 2 X. Go::l X -t 2 X W s X:- 'f. 5 j Y\.)<, 3
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I b-6pt I Sketch the slope field and solution curves for ~~ = x + y 2 . Include enough detail to be able to give a rough sketch of the solution curves with y(l) = 0 and y(O) = 0.5. y ·---~-- -1.5 -0.5 4 ·······/ / 0.5 1.5 X
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Problem 2. la-8ptl Find the (explicit or implicit) solution for xdy- - 2 - = O,y(l) = n. dx cosy . J~ rL I ]i - ZM:J u_~ Jj ::: yt-- s;/ - 2~r--r C 0 O+C 5
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I b-lOpt I Solve xy' + 2 _ 1 y x2 = 0, y(l) = 1. ql-+ b. - \ J x )" - x> / j -e .cc: 2 _Llt< '~ /)j y L \..._ ..::::: >( ( '1.2_.)1 '/ = ·~ xY _,&,x+ C I O+ c "-) - J 6 X
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I c-10pt I Let x(t) represent the number of grams of salt dissolved in a water solution. Assume that x(t) satisfies x' = x- x 2 and x = 0.1 when t = 0 minute. How many minutes will it take for an additional 0.1 grams of salt to dissolve?
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