245ch2testsoln

245ch2testsoln - 'Ltt + ex cin u\ - O Fvqnf . IrT^^ ^-^^+....

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Fall 2007 tath 245 Chapter 2 Test (19 Sept.2007) Name: 6wdt l"tustn Prob. 1. Find the integrating factor I(t) thatallows the l't-order ODE Q + Zt' y = 0 to be written as ll r,,rv(/)l= o. ,il1-,.,.,\.,r Tta ry'n. 4^, & 6* fu4,rg=u. t 'TA ,tq,-% /o"?* a' Irct - ",tf**_ "!;rrr: "iot ctu&' #f ,ifi,,tJ= sit'#r I Ecr\t = ,i? # +s,!t,yf ,o Prob. 2. Indicate in the respective spaces the order of the ODE and state whether the equation is linear or nonlinear. a) !++"ly =5r' orarr, ( f LinearA.,lonlinear: AloflUruh^ ux b) +.9siny = 6cos2x order: X* LinearA.,lonlinear: Nant*o* . ) Lutvq/l\vltllllwq. dx' c) +.9ysinx=0 ora"rt!* LinearA.,lonlinear: L,*^ , ) - revrr F Llrrvq/I\VlulllVcl . dx' ,, dy d'y n* d) 7#*4y = 5t Order: U LinearA.,lonlinear: A(ofll,u^rlil," dx dx' Prob.3. Indicate whether the following ODE is exact or non-exact. You must provide a mathematical basis for your answer. ' dV
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Unformatted text preview: 'Ltt + ex cin u\ - O Fvqnf . IrT^^ ^-^^+. 'rr/ (3x - e' sin y) z - (3y + e' sin !) = 0 Exact: Non-exact: dx rh y i r/*, F,- iltopdy+M6g)dx=o frut * ''/xaclwoo", U-?.4-r' Tr=trr' '# = ft (st'e\*y) = -! - eYeu 6 s#tw g,i =& Gr ^e'sa1)= 3- ero^d Prob. 4. Find the solution of the following initial value problem. (xt + x'y\Q+3x2ytxy' =0, t(2) = l. 'ftn al^. i^ *tu F^ lJr*rip* n "rr5)dr =o. ry = ?JG.!+rg) = B* =& (r3**f ) = Ct^!r!.'f Je 4" A sdd, t^4. f0' elu t't*oct, b k+R, gru^^l soe*J<; Vf*'g = crn(t. usLa^L, Y; Mk,J) = g*b *xJz t{lcx'g) = *i& * + *lt * A,tr) olco, ,Dy = N(x$ = x3+r26 n Vc*'51 =' x\ +*!" r &*) (-JrY"pdr"15 C<.frera_urns, If, W^l f** { Vcr$ )a $o<.5t = * {*'It = cryrct. 3xz +2** ) " | 'ug -'d-!'t Jxa+ 2*3 I 't - * *3g lA* +U Vufr^J La,ul'LiFu\A f,cD=1 , q{;, =+' (rf 1n1.Cz)?.(.1)"= e+fi= lo= cr*ct. *1$ * I rt'=,o,/...
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This note was uploaded on 09/04/2008 for the course MATH 245 taught by Professor Alexander during the Spring '07 term at USC.

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245ch2testsoln - 'Ltt + ex cin u\ - O Fvqnf . IrT^^ ^-^^+....

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