quiz 1 - of this DE y 2xy2 = a and the initial condition...

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Fall 2008 Math 285 Quiz 1: Sep 5 Name: If you cannot complete a problem (perhaps because you forgot a formula) but you think you know how, please describe. Correct methods will receive partial credits. 1. State the order of the given ordinary differential equation. Determine whether the equation is linear or nonlinear. d4R dR - = t- -cost dt4 dt L----- 2. The first-order DE y' + 2xy2 = a has solutions of form 1 y= x2 + c' (a) Verify that y above solves the DE. It- r c '" ( 1. \- L \.':) ~ ~ := -lex: -+ c) .2.-\)( - (b) Find a solution of the first-order IVP consisting
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Unformatted text preview: of this DE y' + 2xy2 = a and the initial condition y(2) = 1. S:e.;-~1. .-tC" I. ~ 4--(-C" L S'o C~-:3 (\'~ <Y\ ~ V I\.r. "\-M. . f'. .Q. C, \ ~ s \ . C;;~ lA o~-s:V\> ; \ 'jC><) ~ 'X~-3. (,J3 ,co) '": ''''c\v&. .e-J 3. Determine a region of the xy-plane for which the given differential "equation would ~e ;;-. / <' unique solution whose graph passes through a point (xo, Yo) in the region. dy x-=y dx ._' 'X:....
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