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exam2F09sol - MATH 216 SECOND MIDTERM EXAM\v Please write...

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MATH 216 SECOND MIDTERM EXAM November 16, 2009\ \}v Please write your name: ___ __,::._---f----\d-------- Section: ----- The test contains 8 problems worth 100 points total. To get the full credit you have to show your work. Problem Points Score 1 12 2 14 3 12 4 12 5 12 6 14 7 12 8 12 Total 100 Typeset by AMS-'IEX 1

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Name: ------- (12 points) 1 p bl F" . ro em. md the solution of the dia: t· 1 . ueren Ia equatiOn II 2 I Y - Y + 2y = sin x that satisfies the initial conditions y(O) = 0, y'(O) = 0. ll 2 \ :::0 '2 r -2v-+'---==-O ')... (r - ' ) -== - l v ::: l -t.. ;\ j "- = c.,/ en X--+ c2 X z':J 1 -t 2-:l "' (- A1 )<- :B=x)- 2(A <hx-_fJ ;..,>J,-2 As;""+- 2 .=:. ffhX A-+ 2 -t-2A ::' I ·-&-2A -t :z..B =0 --, 9-::: 2A _ f\ + 2 (2A 1-+ z A- =-' A= , B"' r c.t z. r- I "X· I j - -; t 171 " -+ 5 z /.ll "' -t f 2
Name: ------- (14 points) 2. Problem. Find all solutions of the differential equation y"' + y =e-x. 3 A _ _l -3 \ x..e 3

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Name: ------------------ (12 points) 3. Problem. Consider the differential equation y" + y = x sin x + ex. If you use the method of undetermined coefficients, in what form will you look for a particular solution y(x) of the equation? You do not have to solve the equation.
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