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## Week 3 Notes Differential Equations

by: Michelle Schmutz

7

0

4

# Week 3 Notes Differential Equations Math 2420

Marketplace > University of Texas at Dallas > Math 2420 > Week 3 Notes Differential Equations
Michelle Schmutz
UTD
GPA 3.3

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examples from the third week of lecture
COURSE
Differential Calculus with Applications to Physical Sciences and Engineering
PROF.
Dr. Anatoly Eydelzon
TYPE
Class Notes
PAGES
4
WORDS
CONCEPTS
Math, Differential Equations
KARMA
Free

## Popular in Department

This 4 page Class Notes was uploaded by Michelle Schmutz on Friday January 29, 2016. The Class Notes belongs to Math 2420 at University of Texas at Dallas taught by Dr. Anatoly Eydelzon in Winter 2016. Since its upload, it has received 7 views.

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Date Created: 01/29/16
Tuesday Lecture €116 --y'x°)G*o 㾎 -to #=× YvD dlABI=rEw¥oD4⊥Iz Hxd iffy \ DO ,B)=µo.jhozxsf eDFirdacurveLSatisfyingthconditioxtuatforlvelypointtontheunvethedistanafromAtoBislqualtothedislanafronBtoO.whesBisthepointyIhtessectionoftayentlineatAwiththX-axis9.jEoytougeutline@xodsf.yq.gy-YotYQdlxthh-jlxohtOcyYbxy-o.yo dlA,B)=d(QB) 㱺y÷u' d4A,B)=d2QB 㱺 " ¥I÷Ex÷÷⾨o ⊥t¥÷B¥¥¥¥¥¥¥¥*f" 㱺y=ux 㱺 }÷iu=2 .uaUY Xo2yo2=2xoy= T.az YKXD 㱺2utu3 Thisistnuforwerypoint f2=Yt¥=u4tuD xd×=uu+uY X2y2=2x" a '=×¥g? Jomfunction y atb=' u¥u=⾨ E=×2ty2 Hymn,dn= dig TI "x±t# - b=2 ##''× xtyzt?_ ' } xztly (E) ffg.zg]dn ¥¥ap㱺 Hisaunot.esolved 1fdx.tn#tlnCfiuyI-udu4\$.IItxx4lytR"=R2=k(CD ^" u÷ uythttbuntgtz bnrurenaitb¥yi • =bn|d 9- =c •P 㱺a(u2¥r(bu+c) uy ×2ty2 ubi)i =µ€ , >× 1u?_ auztatbuztcu are 1u2=( atbjuztcuta therelxistadifferentifunctionfcx,y)suchthat > ? Tf = (xyt ,×2tkgynthtyge . fxy=× Gxax f(× ) fxy=fy× Df=< xyy,×z> fx fy fHXxytlfyx=Z\ ) ,y)=Yzx2ytXtCG implicit fClayx+d\$='zxT )=C ffyyktzxytxtc G) ±x(x2yz+y9=sj ȼ differentiation Hoesy2t×22yy't4y3y' 2×y2+Gz2y+ay3)y1=o D=I××¥Tef 2xy2dxt(2x2ytty3)g=o ×2Y4y9=C W / fxy=4xy fx fy fyxtlxy ex)M(x,y)dxtNk.y)dy=O flay)such that fx=M and then fk fy=N , ,yl=( Sohesthlquation My=N× Differential Exact - Equation Bernoulli Not ideal took , Lecture sinaYswoeldcanalarygFCxiy1.Fxy-FyxMQiy1dxtNlx.yjdy-OMdxtNdye0gMyEtEjMy-FxyMlXidtNkiyyt0iNt-FijxytPCx@NkMyQkihlfthisistrue.DEiseXadex0Cxy2tHdxtyx2dy-OCSolutionisitexact7.y2I2tI2z-c.xEFEEEYI2gIEEIIfixux.eFCxiy5SNdy-Syxzdy-y2gItCWIDXtCkxKMsbrfcYIYIu-x2ztcFK.yty2I2tEztcex20My-Caesy1yosinySobtionNx-Cy2-xsiAyb-sinyx7tYY3-cFlxiDtfcosydx-Xaesy-cCyj3xaosyty3-cFy-tsiJnytdlyKyz-xsirxclyt-y2.Clyky3gtCEquationisIxactifthereexisbFlx.y suchthatfx - Maud . ) Fy=N FXy=Fy× If e×3O2ydxtxdy=0 FK ,y)=f2yxdx=yx2tC(y) Mfftxor Myffk is function My=2 , Nxt 㾎 Fy=×Y+c'ly)=K one variableonly,then DE can notlxact )=0 of ( Cky . 2ydxt×dy=o)*× Cly)=C hyxdxtxzdyio #yx㱺,, My=2x,Nx=2x Flxiy ) ),then µW=eshHd× betwmedinto(xmakesequationsthat ) IfMyyN_=hk Fty.yx=o .. If Nx. Shly)dy My Nx= My ),then Mlyl - -M=hly (km '=Pkj # ,µk1=ef¥=x fy 'Iy+dly)=±g Nx. ' " )=o Ny -toy ,µly)=e "2bny=y' 2=4 Cly _µ=lzt= c by)=c 3¥dxtIgdy=o My=¥ ,N⾨Yb 2×ry=c eDmy¥×=2×I=×t FCX 2ryd×+§dy=o ,ykfMdx=f2ryd× ×rY=o Yxt =2xrytqy , ex ( ytxldxtzydy -0 (y2×)e×dx+2ye×dy=O FKHF My - ay ftp.xlexdx-SCyzex.xexjdx µ×=o M#V×=3j- 㱺 - 㱺y2e×-×e×te×tCly) µCx)=eId×=g ) Fy=2fe×tdlyKX× CYYKO yYte'e#T

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