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# Ordinary Differential Equation MATH 3230

GSU

GPA 3.94

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This 7 page Class Notes was uploaded by Miss Emerald Langosh on Monday October 12, 2015. The Class Notes belongs to MATH 3230 at Georgia Southern University taught by Staff in Fall. Since its upload, it has received 41 views. For similar materials see /class/222048/math-3230-georgia-southern-university in Mathematics (M) at Georgia Southern University.

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Date Created: 10/12/15

Math 3230 Review 1 Namp F Ziegler Show your work to receive credit and your nal answer in every computation Spring 2010 For each of the following equations state Whether it is linear and nd its order a g 2ty mm lt 3 In Wm nmi v r dt tZy first water chh39vgth39w Ihw wal amp 6 bal AgvM craftingv grayish g t d4y dy yum 05 QIL JIEJ M Mm M a b 227154 759 2ty 3 lm ML WW 43 mt nm l R wl Mawkw Mv wak F m I Z no ICMKLL KW d2y dy 2 nmexMaV 6 k n c 2yt 2 MW we or M clt2 alt Sum W K 4 th 3 ukVQh lt 2 For each of the functions y1 ac and yg 2 at b2 determine if it is a solution the differential equation If so nd for which value of a and b it solves the initial value problem y0 2 y 0 3 z 2 2 a 2yy y 2 242 tat 9a tub m 2 Mm rgt 42 vs a s1 ng W a W quotiiiilfhfiixf he WWW w ca 2 1 a 2a IVF Lilla a 5 3 LAN a gt di39o Zaln 3 L gh L4 tz aibl a quot 03quot 1 b W y 2 a Me I M m H 39L ht 1 i9 Moi I41 lm39t mam are If glut3 393 539 Ki 3 NF 2 4 z SCIuh do ab 3 L36 T Zenx2 El Fy in 3 Write the second order equation as an equivalent rstorder system d s the indicated variables wher What is the function WWW MMGM WVS P37 Lie a 7 163 y s t H M39s W t We 539 Cl NW fill at we M U lU l t a i 7 Utah 122 H v 1 x w zmwhereais xed y 12 st t X at a acm v b V 39K 1 2 dzfctt i MMH agt M M 0 my 0 0 BET gt1 M t d2 d 7 c T 6 45 3 a s yomr choice In C f MW 7 v t aw 3 h a 1 9 X 7 AxM f lt 39039 gt if 4 OH M V7 fluQM dartMlquot 61IIirf X t mm mm nore rm 2 2 Fltxgtlt v whath 39ds 0 604 tx a a 1 5 3991ch rs Hu i W 3 1 I MFLITA a Mtr i7 4 Solve the separable equations A5 5 a ty1t2 l 4 E 39f M 3 3 f4 S b tyy2l Fume gmm aucmpogm E xi 3 4 9 I L l MWH 3 13 Byt D quotII C i39 O t ZWH S cga g 333 v 3C t quota QRH C a t 49mg J S 29 w w mg Mum 14111 L mm C P C 7 c we r W dHE ZhM UL 0 er Ui t e El t gziSEEJLt VL dru quot 7 r r 7 m 1 t I red he Lt13 litel 39e 392 39f C 5 For each of the following equations determine Whether it is emact If so nd its solutions in implicit form widt ilidyzo C I M N r all M l 0 hame 1 8 MM 5344ka aka at 1 fov W V0604 as C l t 3 SMt0 dt g Mum S to z 5 b ysintht cos2tdy 0 T T QM 0N J V 3m 2f Plat Erkaot 2 6 SMZL39 I ZSHZE c cost3t2ydtt3 y2dy0 tSl nt 935 v J V J r mm M N i 5 am impAmi 5mm in fai 1 r l 2 V414 0 C M 91 39 3 Sill 0 3 WWW 9 M t w ti V 3 quot i 3 1 g n 3 l a So ClolgoN3AA gf Smk t4 EQL s t 3 Sta St kl dz 6 Consider the equation 1 t2 a Rewrite it as an exact equation M dt N dy 0 Th m thAbi Zia3535 HMUM 4 Q WV 37 Hz O z W n IWOL CCt gabt b Find its general solution in implicit form t gmhopw mayan P M w L W I G Ll HY i ll t1tgc31 WWW a H W4 Mth m MM C w rm Math 3230 Review 2 Name F Ziegler Spring 2010 Show your work to receive credit and your nal answer in every computation 1 Solve the homogeneous initial value problem y 7y 10y 0 y0 1 y 0 5 Chm a H 7r I0 r2rs 0 1 3 emupale Zeta at f quot t l Sale c ilt5 l gtlt gt CLgt 3 392 I j Lil I 5 2 Solve the homogeneous initial value problem y 100y 0 63 00 rOL39 wlon l g0 C1 310 X39s gt 2 ZC SOL 5 Cl C2 1 2395 r7 loft C my awn wt vra c 139 39i c39 lzp 3 396 2 R a 397 I L CL 139 d m k3 d39ws0f jasmm l I Srlnce j 0d 5 M lOaLOOJUOt X cosx H smx e cosx L39Mlt l W at I M wva A L Mo 0011 to 6quot e 6 K SMK 7 Lt J M LB3 We 5 de 4quot SWd MFA cmrcw XPMWHQLSW 39 arrive I39WHEnal hg I it of 539 bwi cmtt39mlw SrVHPLLY Mu 39ii r 39 d 3 Find the general solution of the inhomogeneous equation y y 2y 1 l gt Hm Que 523 O Wet F2 1quot Z kW 70 O 2 amp m 397 2l 3 gt 3 96 ole b 3nfgtwmz mm mm the m JAM puma e Pm VvCH xno mil amt 0 2 ma PM 139quot I Q Lita WinnH hug 60bAA 912 3130 39 Sawx Emma 5 I be Wz 00 2A l l39 o gul39I39 f i 3 PM Mm 5 W inimwwVEMWWM 2quot Wl swat i j 39Z ce 96 We at 4 Find a particular solution of the innornogeneous equation Mil 553quot coset Hm 3 Z 0 axij r1 3r 2 INN2 o t v 39 3 96 626 2 Cumegg Ell L41 6 neat t Zt l l 2t w W at le39b 45 391 2l 393 7 3mm RHs 3f 3901 Wm e Pm We lg equot 1 A1 5 Li t4 4 M1 L1 VM CommaH Zt t Wk W aziwzgw n SebwsefaVc lL S W 6 3t M a S CosULMM EMU z svncb t u Mpg 150w 2 7 89 comma SM 03039qu E ussnm 3 summer dlgm lag PM H usmO 04M3 t e sIngg 62tfebsl39ncet comm ebswelj mum t 7 V 3914 cur 6 wet 39 e tsMel quot e Ham 2 oosat llxl 4 H H 5 Consider the inhomogeneous equation y t391y t2y 1 011 homogeneous equati I i I l t 39 t n o a Check that y1 t is a solution of the corresponding nd another linearly independent solution yg WAC 1 2 0 gt Otquot t 1l O I l IIHde 0 M13 S m WWW Wt W S W M iz LQII UL lamb FPISGES39 gt A inqu l3th i3quott lg39 chCVOL 0 H t HM e tHA lt wt dcrdvc deh39vc 1 n I Le Mt2m u u t u u t3u 0 r U i ULl 5 M r l L T t La T t Sir M Stat gt mCu 3 amt gt MI amt Eva A S A 6M 1 t392 puma Wt f w Si39mlo qHa J 5 quoty 932 Mi 3 tquot Huck z l H39v 91 25 kw 0 gt3 1 No 2 t l gt t w nd the general solution of the inhomogeneous equation b o m equalWm WW Comm mgmm Voth ah w o WW W Ld zult39all39lMlk WW k l t I fizzy 3925quot W Hf 0 is a Have we v gm aimquot gm WWW WM Math 3230 Review 4 Name F Ziegler Spring 2010 Show your work to receive credit and your nal answer in every computation 1 Recall that a two loop LRC circuit as pictured is gov erned by the linear system 1 mg I 1 z 1 E t dt RlcQ 2 R1 112 1 R Q IZHZ R11 L1 quota L ciQ T Q 31 where Q is the capacitor s charge Here Q 1 I2 I7 E and EU R 3 LR1R2C 113 1 are measured in the standard 391 units Coulomb Ampere Volt and Henry Ohm Farad 2 EH Iv H a Find the eigenvalues and multiplicities of the corresponding homogeneous equation a lt 1 B l l gt 6L J A H AI 17x3l 13 W2 0 l 3 C A W 3 39 Wn39i h hr Z I b Find the general solution of the homogeneous equation M if Igtlt gtlti3gt em w W m gum seam Noam Wm QMZIW r w wltgt swam 39uteJgt m we 2 er mm uh amp airMrle

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