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Exam 1 Li Spring 2011

# Exam 1 Li Spring 2011 - 1 EXAM 1 MATH 2233 SECTION...

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1 EXAM 1 • MATH 2233 SECTION 002~.SPRING 2011 INSl p L/- 0- . SHow~WbRK FOR CREDIT I!! SHOW WORK FOR CREDIT !!i ~I) (5pts) State the ORDER, LINEAR OR NONLINEAR of each of the following differ- V entia! equations. ,n/ a. t4~+~+~.y=esmt. ? _ D~ / )~ C -'L;"Clt0 r--., / b. 'f,JI+y'fit-t+I=O. 2~ @ L~~v- ~.C:2 (lOpts) Determine the equilibn m-solu ns, and classify each one as asymptotically stable, unstable or semistable. ~~= -2y(y-l)(y+ 1)2. ::: .('(~) ./; -_."

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2 WEI PING LI (3) (15pts) (a) Draw a direction field for the equation ty' + (I + l)y = 2Ie-', y(l) = a, I> O. r 2 t K! I I a, ~ vlf"tIA >d l;<A1b~ ~~td1 Wl1b~ - 0... -= e = a ~ ~ ()./'~~ z.e.Y"O I
DIFFERENTIAL EQUATIONS 3 (4) (10pts) Given the homogenous solution y = Ce- t ' for the equation y' + 2ty = O. Solve the non-homogeneous differential equation, by using the variation of constant method, y' + 2ty = 2te- t '. ClY1 iA 11 ) t~ s 1,)( w/~ I~-&<C..tt, -/4. re. e.'( I'; Jc; ., J'\ -I Q.YV&I\ -I- t;{l .- (5) ~etermine (without solving the problem) an interval in which the solution of the initial value problem is certain to exist. (t-l)(t-4)y' +y= 0, ~= 0 .j .. J L.j.- ~ -I OCt ~,J\ L.f- 4 \ -:: 0 ,/J &r~: I (J [,() - 0 & -/)(,"- '1\ ,

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~0 DIFFERENTIAL EQUATIONS ' ~ (8) (lOpts) Solv~exact e uation ) , , . . (2x + 1) + (2y - 2)y' = O. , 11\' \.. . , . (fYI'j'~' , ~-",'I -- 7' '"' -/' .. .; ;-~~ f11~ = 0 ;J'r- 0 ~ r('f(,'J\: 1i't1(7fI~') fA", :/ i,!~if!"-L .' . '1~.f- '}( ~L (~Y 2."tI) "d'J -\ ~;; 0 + c.. Zij)

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