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
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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/~ .tt, -/4. re. e.'( I'; Jc; ., J'\ -I Q.YV&I\ -I- t;{l .- (5) ~etermine
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Exam 1 Li Spring 2011 - 1 EXAM 1 MATH 2233 SECTION...

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