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plugin-ch4soln - Math 245 4 Chapter Test(Feb.25,2009 2009...

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Spring 2009 Please check your discussion section: n llam n 12pm r lpm Jof Sovns' 1 o,,\4. FS\ I Prob. 2. (lOpts) Write the quantity y = -Ji cos3r - sin3r in the formy = Rcos(a/ - d), where Randthe dareallpositivevalues(n>0 and d>0). Showclearlytheprocessofusingthe trigonometric identity. t = z { + L o $ 3 t t J s * =Z t ^tT c"\jt +$vn$ = r Lrstrt-+) 4 .. I f*rt J Math 245 Chapter 4 Test (Feb.25,2009) Su.t- Mol"tP''r Prob. 1. (10pts) Solutions of a linear 2nd order ODE are given by yr(t) = t2 and yr(t) = t2lnt . Determine whether they are the fundamental set of solutions or not. r,v = ll ;i \= lI ,iil--.| = y)M.t3-ut*r:r3 ) \/\I ro ) t' ,1.'
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Prob. 3. (10pts) Write the complex number , - 5-t+2i in the form a + ib . Z = | ehs]-t+ie- -/^s +itL,,f :.{^.s oio.hr _ t{,"ste0*s) ti i^taLs)} / = e = g e = - , r - t r Y ' t \ < r ' ^ " ' J f u / / Prob. 4. (10ts) The characteristic equation for a homogeneous 4th-order ODE is given by: (D"+r)'U: -4x"+13)=g. Write the general solution of the ODE in real-valued form, and determine whether the solution is asymptotically stable or unstable as t + o.
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