Exam 2 Li Spring 2011

# Exam 2 Li Spring 2011 - c~~ (6) (lOpts) Use the method of...

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1 EXAM 2 . MATH 2233 SECTION 002, SPRINCbOl1 INSTRUCTOR, \' Print Name SHOW WORK FOR CREDIT !I! SHOW WORK FOR CREDIT I!! (1) (15pts) (a) Solve the initial value problem: " 5, 3 y -y=O, y(0)=4,y(0)=-4' ,,--2-1-:: 0 t: I +- -e- f;:;~ ""0 !V\(J;ef ~ e-t-) -c - z. IV! '-:; - ~ Z-t. . -:. 'Z;. ., 2. 1! '=- I"", ?J ~ . 61/ "3 (b) Determine the minimum value of the solution. (You n en to verify it is ml imum) @ ...... ,..... ,.,Mi~\.l.,. .,. ...., r= -I ) ri. . = / I -t of-Ce.* /'~ - C,e ~ I • to C~ e. ~ '~ lj ~ -( ,e.+- ~'-- (, ~ .f.(" -kt-= t -C, + c. "t ~ j C, :- J c. t '; .kt -:::.)

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2 ~ WEIPING LI (2~S) Verify that two solutions YI(I) = e' and Y2(1) = Ie' of the differential equation Y" - 2y' + Y = 0 form a fundamental set of solutions. 1. ~ I 'h, A "W' ~ ..f~u.d r:; (;~ 5L{vlt~ '\ '." \~'f' .~ r-j'';-,F' 0''?; t (3) (lOpts) FInd the general solution of t 2. ~ ( _ 2. r- r I ~ 0 L1 /'l~ d I -; ~ l '1-=- (I et-: 0J \
DIFFERENTIAL EQUATIONS 3 (5) (15pts) conside~aJ value problem y" + 2y' + 2y = 0, y(O) = 2, y' (0) = Q. r Z. of 2 (j'" -z. . -Z-:t~q- q r-:- "2. . (i) Find tbe solution y(t) of this problem; (ii) Find Q so that y = 0 when t = {. r "-----

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WEIPING LI 4
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Unformatted text preview: c~~ (6) (lOpts) Use the method of reduction of order to find a second solution of the differential equation DIFFERENTIAL EQUATIONS 5 (8) (lOpts) Identify p(t), q(t), g(t) of the following second order differential equation, determine the largest interval so that the equation is certain to have a unique twice differentiable solution I ~..4.J?, +. '; ",.1.,; -I ~"M o ~ f<t' . +h-., i "S r~ '-t M '-.AIL C) ...Jw)c.e. d:fk,,,,,~ ~ ,,() Iv. .+"owl t-~Vl }:V\.~r--wtL Wiry;~ =) [-oG' <-e-.( ~ (9) (lO~ts~frihe Wronskian W of f and 9 is t 2 e', and f = t. Find g(t). IN (-4'\ ()'):: .{' :/ ~ . .(' r~-t '- 4--r ---t 1";. I ,L-a)" -llL, ~ .(le "-~ 1-: {" ~ ~ te t-]ut)/ ~. f-):: f-ee . .f: 5-f ::: ,J t1. e ~ 0/. f J f:-e~' ( of "L_ Z. of . '2. \-rL l try :: e. *--c-I (-t "!. -'Z i of '2- ')-1-?& j...
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## This note was uploaded on 01/10/2012 for the course MATH 2233 taught by Professor Binegar during the Fall '08 term at Oklahoma State.

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Exam 2 Li Spring 2011 - c~~ (6) (lOpts) Use the method of...

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