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1、常微分方程求解技巧（Solvingtechniquesofordinarydifferentialequations）No.Volume322journalofchinawestnormaluniversity(NATURALSCIENCEEDITION))2011JuneVol.32No.2JournalOfChinaWestNormalUniversity(NaturalSciences)Jun.TwothousandandelevenArticlenumber:1673-50722011)02-0
2、190-03SomesolvingtechniquesoffirstorderordinarydifferentialequationsFengShiqiang,GaoDapeng,ChenYoujun,ZhangShilu(Schoolofmathematicsandinformation,ChinaWestNormalUniversity,Sichuan,Nanchong)637009)Abstract:thereisnogeneralelementarysolutiontothefirstorde
3、rordinarydifferentialequations.TheseparationofvariablesandthetotaldifferentialequationarethemostbasicofthefirstorderordinarydifferentialequationsInthispaper,thetransformationofthesetwotypesofequationsisintroducedwithexamplesTechniquesandlawsKeywordFirsto
4、rderordinarydifferentialequation,transformationSkillsCLCnumber:O175.1documentidentificationcode:A1IntroductionWhenwestudytheordinarydifferentialequationtheory,wealwaysfindtheseparableequation,homogeneousequation,homogeneousequationandfirstorderlineardiff
5、erentialequationBernoulliequation,differentialequation,solutionofequationsofdifferenttypesoffirstorderpartialdifferentialequationtothecombinationofdifferent.AdifferentialEquationscanfindthetypeoftheoreticalsolution,orthevarioustypesdescribedearlier,orbyi
6、denticaldeformationorequivalentdeformationcanbeconvertedintotheaboveclassOneoftheequationsofthetype,thearticleisjustanexampleofthe"transform"Techniquesandlaws2severalimportanttechniquesandexamplesTwo1intoDdyxForddxyIfthedifferentialequationis(orconvertib
7、leto)(DYFX,y)(GX,y)DFX(X=,(GY)X,y)DyDXWhen(fX,y)(GX,y)simple(oftenaboutafewfactors)variableDXbyDy,atthispointtheequationbecomesDX=(GX,y).(DYFX,y)Afterthistransformation,theequationmaybeaclassofequationsintroducedearlier,ormaybecomeaclassofequationsDy2XYe
8、xample1equationDX=X2+YGeneralsolutionofThesolution(fX,y)=2xy,GX,y)=X2+Ysotheoriginalequationdoesnotbelongtoalltheequationsdescribedearlier,but(GF(Xx,,YY))=2xy+Twenty-oneX,soDdyx=2xy+Twenty-oneX,revenuertoDdyx2XY=Twenty-one
