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首页 二次微分方程的通解

二次微分方程的通解.doc

二次微分方程的通解

幸福既那么近又那么远
2017-08-29 0人阅读 举报 0 0 暂无简介

简介:本文档为《二次微分方程的通解doc》,可适用于职业岗位领域

第六节二阶常系数齐次线性微分方程教学目的:使学生掌握二阶常系数齐次线性微分方程的解法了解二阶常系数非齐次线性微分方程的解法教学重点:二阶常系数齐次线性微分方程的解法教学过程:一、二阶常系数齐次线性微分方程二阶常系数齐次线性微分方程:方程y,,py,qy,称为二阶常系数齐次线性微分方程~其中p、q均为常数,如果y、y是二阶常系数齐次线性微分方程的两个线性无关解~那么y,CyCy就是它的通解,rxrx我们看看~能否适当选取r~使y,e满足二阶常系数齐次线性微分方程~为此将y,e代入方程y,,py,qy,得rx(rprq)e,,rx由此可见~只要r满足代数方程rprq,~函数y,e就是微分方程的解,特征方程:方程rprq,叫做微分方程y,,py,qy,的特征方程,特征方程的两个根r、r可用公式,p,p,qr,,求出,特征方程的根与通解的关系:rxrx()特征方程有两个不相等的实根r、r时~函数、是方程的两个线性无关y,ey,e的解,这是因为~rxye(r,r)xrxrx函数、是方程的解~又,,e不是常数,y,ey,erxye因此方程的通解为rxrx,y,CeCerxrx()特征方程有两个相等的实根r,r时~函数、是二阶常系数齐次线性微分y,ey,xe方程的两个线性无关的解,rx这是因为~是方程的解~又y,erxrxrxrxrxrx,,,(xe)p(xe)q(xe),(rxr)ep(xr)eqxerxrx~,e(rp)xe(rprq),rxyxerx所以也是方程的解~且不是常数,,,xy,xerxye因此方程的通解为rxrx,y,CeCxe(,i,)x(,,i,)x()特征方程有一对共轭复根r,,,i,时~函数y,e、y,e是微分方程的两个线性无,,x,x关的复数形式的解,函数y,ecossin,x、y,e,x是微分方程的两个线性无关的实数形式的解,(,i,)x(,,i,)x函数y,e和y,e都是方程的解,而由欧拉公式,得(,i,)xxy,e,e(cosxisinx),(,,i,)xxx,isinx),y,e,e(cosx,xyy,ecosx,,ecos,x,(yy)x,xy,y,iesinx,,esin,x,(y,y)i,x,x故ecos,x、y,esin,x也是方程解,,x,x可以验证~y,ecos,x、y,esin,x是方程的线性无关解,因此方程的通解为,xy,e(lineofthebusthroughthelistofmadeamoredetailedprovisions,applymoreoperationalSevenisincreasedthearticle,inviolationoftherelevantprovisionsofthe,toparticipateinpublicfundstopayfordinner,highconsumptionofentertainment,fitnessactivitiesandpublicfundstobuygift,sendgiftstomaketheprovisionsofthedispositionOntheviolationofthecentralprovisionsofthespiritoftheeight,inadditionto><newregulationsinto"violationofhonestyandselfdiscipline"misconductoutside,isdifferentwiththeoriginal<Regulations>,revised<rule>clearlydefinednotonlytodispositionofthedirectlyresponsiblepersons,butalsodisposeofcollarGuideresponsibilities()increasedtradingrights,useofauthorityorpositioninfluenceasrelativesandclosetoprofitviolationofthetermsofthe<NewRegulations>absorption<cleanpoliticsseveralguidelines>therelevantprovisionsspirit,increasethe"negativelist,includingtradingrights,thefunctionsandpowersordutiesofinfluenceasrelativesandstaffaroundprofitIncreaseArticle"mutualuseofofficeorauthorityringforeachotherandtheirspouses,childrenandtheirspousesandotherrelatives,aroundpersonnelandotherspecificrelationshipbetweenthepeopletoseekbenefitsengageintradingrights,givenawarningorseriouswarningSanctionsifthecircumstancesarerelativelyserious,givingremovedfromorplacedonprobationwithinthepartypostifthecircumstancesareserious,shallbeexpelledfromthepartyIncreaseArticle"connivance,acquiescencetothespouse,childrenandspouseetcrelativesandstaffaroundtheeffectofPartymembersandcadrespersonalauthorityorpositionforpersonalgain,ifthecircumstancesarerelativelyminor,givenawarningoraseriouswarningifthecircumstancesarerelativelyserious,givingremovedfromorplacedonprobationwithinthepartypostifthecircumstancesareserious,thegivenExpelledfromthepartyPartymembersandcadresofthespouses,childrenandtheirspousesdoestheactualworkandgetsalaryoralthoughtheactualworkbuttoreceivesignificantlybeyondthesameranksalarystandard,Partymembersandcadresinformedfailstocorrect,inaccordancewiththeprovisionsoftheprecedingparagraph"()aboutthegifts,giftsmisconductfromhandlingpracticesinrecentyears,engagedinofficialcadresreceivedgifts,giftsproblemsmoreprominentThishasseriouslyaffectedtheimageofPartymembersandcadres,damagedtherelationsbetweenthepartyandthemasses,andisahotbedofcorruption,isreallynecessaryforthiskindofbehaviortobedisciplined<rule>noonacceptinggifts,gifts,Cardconsumptionbehaviortoengageinsimple"onesizefitsall",butthedifferencebetweenthedifferentseparatelyOneisinaccordancewiththeprovisionsofArticle,acceptingmayaffecttheimpartialenforcementoftheofficialgifts,gifts,consumercardstodependingontheseriousnessofthecaseshallbegivendisciplinarysanctionsThatistosay,formayaffectthefairexecutionofbusinessgifts,gifts,consumercardsarenotallowedtoacceptisinaccordancewiththeprovisionsofArticle,acceptingwassignificantlyhigherthannormalceremonyisstillexchangesofgifts,gifts,consumercardtodisciplinaryactionThisisnewregulationsthatdailylifeispurelyreciprocity,acceptingthesamething,boys,fellowfriendsgifts,gifts,shoppingcards,althoughandfairexecutionofbusinesshasnothingtodo,alsowanttoasthecaseshallbedealtwith,thesituationisobviouslybeyondnormalreciprocity"Thesocalled"reciprocity",oneisemphasizesthereciprocalinprotocolInotherwordsisyoutomehow,Itoyouhow,notonlydoesnotgoThesecondistosignificantlyexceededthenormallocaleconomylevel,customsandhabits,economiccapacityofindividualgifts,giftvalueSpecificsanctionstoaccordingtotheprocessingofavarietyoffactorstoconsider,asappropriateThethirdistherootaccordingtotheprovisionsofArticle,"toEngagedinpublicservicepersonnelandtheirspousesandchildren,children'sspousesandotherrelativesandotherspecificrelationshippresentedMingXianchaonormalreciprocityofgifts,gifts,consumercard,ifthecircumstancesarerelativelyserious,givenawarninguntilprobation"Inaccordancewiththeaboveprovisions,giftgivingsignificantlybeyondthenormalreciprocity,giverconstitutethediscipline()onillegaltradingofstocksorofotherregulationsofsecuritiesinvestment<>ArticleisengagedinpunishmentregulationofcampandactivityinviolationoftherelevantprovisionsonAmongthem,will"buyingandsellingstocksorinothersecuritiesinvestment"columnasoneofdisciplinarycasesOutFirstneedtobeclear,><regulationsdidnotchangetheprovisionsoftheOrdinanceTheordinanceoftheprovisionsofthesecondparagraphofArticleprovisions"who,inviolationoftheprovisionsofthesaleofstocks"isoneoftheviolation,andatthebeginningofthefirstparagraphofthisarticle"violationofagainsttherelevantprovisionsofthe"textualrepresentationoftherepeatrevisionIn,justfromthelegislativetechniqueremovedthe"personal"inviolationoftheprovisions,contentandnottochangetheoriginalprovisionsNeedtoclearis,"buyorsellastockorofothersecuritiesinvestment"referstoviolationoftherelevantprovisionsreferstoinApril,thePartyCentralCommittee,theStateCouncilpromulgatedtheOntheworkofthepartyandgovernmentorgansstaff'spersonalinvestmentinsecuritiesifdryprovisions>AccordingtotheprovisionsofArticle,useofworktime,officefacilities,thesaleofstocksandsecuritiesinvestmentfundbelongstoillegalbehaviorThefourthquestion,abouttheviolationofthemassesofthedisciplinaryactions<newregulations>wouldviolatepublicdisciplinebehaviorofasinglesetofaclassofrestored"threerulesofdisciplineandeightnote"inthedisciplineofthemassesofexcellenttraditional<NewRegulations>Chapter"toviolatethemassesofdisciplinaryaction",mainlythedestructionoftheparty'sclosetieswiththemassesofmisconductmadeprovisionsondisciplinaryenrichandperfectthesuperstandard,beyondthescopeofXiangQun<Alltoraisefundandlabor,inforinvolvingthepublicaffairsdeliberately,chinakayao,insocialsecurity,policysupport,disasterrelieffundsandmaterialsandothermattersassignedanykindandaffectionatefriends,obviouslyunfairactsagainsttheinterestsofthemassesofthedisciplinarytermsincreasethetermsnotinaccordancewiththeprovisionsofthepublicpartyprovided,government,factoryandvillage(neighborhood)providedetcviolationofthepeople'srighttoknowthebehaviorofthedisciplineThefifthissue,ontheviolationofworkdisciplineviolationofworkdisciplineadded"negativelist,includingPartyorganizationscarryoutstrictlyMainresponsibilityforpoordisciplineterms()thenewpartyorganizationcomprehensivestrictlythemainresponsibilityofthepartydoesnotfulfilltheorperformpoordisciplinaryterms<NewRegulations>hasaleadpeopletopayattentiontothenewterms,thatis,inchapterten"ontheviolationofworkdisciplinebehaviorpunishment"increaseintheonehundredandfourteenth"partyfailtoperformcomprehensivestrictlythemainresponsibilityofthepartyortoperformcomprehensivestrictlythemainresponsibilityforadministeringtheineffective,resultinginseriousdamageorseriousadverseeffects,tothepersondirectlyresponsibleandtheresponsibilityofleadershipandgiveawarningorseriouswarningThesituationisserious,givingremovedfromtheirpartypostsoronprobationPunishment"HerethechangesForthefirsttime,themainresponsibilitywrite<rule>()newshallreportdoesnotreportorfalsereportingdisciplineshallincreasethebar"inthehigherlevelunitstochecktoinspecttheworkorreporttotheparentunit,workreportofshallreportthemattersdonotreportordonotreport,causeseriousdamageorseriousadverseeffectsof,tothepersondirectlyresponsibleandtheresponsibilityofleadership,togivewarningoraseriouswarningifthecircumstancesareserious,givingremovedfromtheirpartypostsorplacedonprobation"Forexample,duringthetourvisitstotheregion,theunitMemberstheobligationtotheinspectionteamstoreflectthetruesituation,toconcealnotreportedorintentionallytotheinspectionteamstoprovidefalseinformation,causingseriousdamageorseriousadverseeffectsof,thepersondirectlyresponsibleandtheresponsibilityofleadershipshouldbeinaccordancewiththeprovisionsof<rule>Articletogivetheappropriatepunishment()thenewnotgrantedinaccordancewiththeprovisionsofpunishment,notaccordingtotheprovisionsoftheimplementationofdisciplinarymeasuresviolationoftheprovisionsofArticle"Partyorganizationshaveoneofthefollowingcircumstances,thedirectleadershipresponsibilityProbation:membersweresentencedpunished,inaccordancewiththeprovisionsgivedisciplinaryactionorinviolationofstatelawRulesofbehaviorshouldbegivendisciplinarypunishmentanddisposeofdisciplinarypunishmentbydecisionorcomplaintreviewthedecisionmade,notinaccordancewiththeprovisionsoftheimplementationdecisionsonpunishmentoftheparty,position,rank,andthetreatmentofthemattersPartymemberssubjecttodisciplinaryaction,notinaccordancewiththecadremanagementauthorityandorganizationalrelationshipsofbydisposeofPartymemberstocarryouteducationandsupervisionofdailymanagement"Whatneedstobepointedoutis,"cliff"demotedwithcars,housing,secretaryproblem,implementationisnotadisciplineandpartypostsandrankstreatmentbytheorganizationdepartmentisresponsiblefortheimplementation,withcars,housingbythelogisticsdepartmentisresponsiblefortheimplementationof,JiCommissionresponsibleoversightresponsibilitiesThesixquestions,abouttheactsviolatingthedisciplineoflife"inviolationofdisciplineoflifebehaviorpunishment",mainlyto"fourwinds"problemsandaseriousviolationofsocialmorality,familyvirtueactsofmisconductmadeprovisionsondisciplinary,anincreaseofextravagantlife,contrarytothesocialpublicorderandgoodcustomsdisciplinarytermsWorthmentioningis,><RegulationsinArticleabout"adultery""mistress(Cardiff)formulationinthenew<rule>isremoved,toexpandthescopeofArticleprovisions"andothershairimpropersexualrelations,letfacedisciplinaryactionWidermorestrictFour,andearnestlydoagoodjobinthe<code>and<rule>implementsystemoflifeliesinexecution<code>and<Regulations>isPartyorganizationsatalllevelsofastrongconstraintandallPartymembersfollowLearningandimplementingthe<code>and<rule>ispartycommittees(party),commissionfordiscipline,disciplineinspectiongroup),themajorityofPartymembersandcadresofthecommonresponsibility,mustpartycaughttogether,thepartyoneexecution()Partycommittees(party)andplayandimplementcomprehensivestrictlythemainresponsibility,paysspecialattentiontothetwopartyregulationslearningcrosspenetrationOneistoAdheretothepartyconstitutionisfundamentaltofollow,andresolutelysafeguardtheauthorityofthePartyChapterThesecondistoadheretotheproblemoriented,tostrictlypoliticaldisciplineandpoliticalrulemomentsinthefirstplaceThethirdistoadheretothedisciplineandrulesquiteinfrontmustnotallowthebottomlinetobreakthedisciplineThefourthistoseriouslyorganizethestudyofpropagandaandeducation,inthecitypartymemberstocreateadisciplined,abouttherulesofthestrongatmosphere(II)CommissionforDisciplineInspectionatalllevels(DisciplineInspectionGroup)toanimportantbasisfortherevisedtwopartyregulationsas,adheretoeasilyblame,strengthensupervisionandenforcementAndearlymethodincombiningJi,increaseaccountabilityeffortsOneistotworegulationswithinthepartyimportantbasis,adheretothepartyconstitutionduties,withstrictdisciplinetomaintaintheconstitutionauthorityThesecondistoadheretohighstandardsandkeepthebottomline,adheretoJiYaninlawanddiscipline,thedisciplineandrulesquiteinfront,graspinggraspingsmall,easilyblame,comprehensiveuseofsupervisionanddisciplineof"fourkindsofform"inthedisciplineembodiesthestrictrequirementsandcareforthediscipline,tightenup,YanAccordingtodisciplineinaccordancewithregulationstocarryoutdisciplinaryreviewIncreasetheviolationspunishment,cluescaninitiateaninvestigationonthetrialofcasesAccordingtothedisciplineontheprovisionsoftheproportionofprocessingandcontrolmanagermaintainsdisciplineTofocusoninvestigatingnonconvergence,don'taccepthandseriousdisciplinaryviolationsatthesametime,paymoreattentiontothegeneralreviewofdisciplinebehavior,andgraduallyincreasethelighterpunishmentFouristoilluminatetwopartyregulations,combinedwiththelocaldistrictoftheDepartmentofpartyconductLianzhengtorelevantlawsandregulationssystemclean,timelyresearchproposestoestablish,change,wastereleaseopinion,avoidconflict,andthefastensystemofcage,andgraduallyformednotrot,notrot,notwanttorotsystemandworkingmechanism()theleadershipofthepartymembersandcadresshouldplayanexemplaryroleTherateofhigherconsciousnessofthefrontoftheOrdinancetoleadpracticeselfdisciplinenorms,leadingtomaintaindisciplineofseriousnessandauthorityOneistheaboverate,demonstrationandguidance,taketheleadinlearningandmasteringthe<code>and<>therequirementsandregulations,dothedeepunderstanding,learningtouseThesecondistoplayanexemplaryroleinabidingbydisciplinerate,taketheleadinpracticingselfdisciplinenorms,firmlyestablishbeforethedisciplineareequal,thesystemhasnoprivilege,disciplineisnoexception,andconsciouslydostandards,requiremorestrictmeasuresmorepracticalThirdistoconsciouslyacceptsupervision,conscientiouslyparticipateinthedemocraticlifeanddebriefinghonestyresponsibility,suchasRealtothepartyorganizationtoreportpersonalmatters,andtoacceptthesupervisionoftheworkandlifeofthenormal,habitsunderthesupervisionoftheexerciseofpower,tocarryouttheworkThefourthistosetanexampleforthestrictenforcementofdisciplineLeadingcadresshouldtaketheleadinthemaintenanceofdisciplineofseriousnessandauthority,todaretoseriously,daretostruggle,daretooffendpeople,formisconductnotlaissezfaire,butdonotindulge,nottoleratetoensurethepartyconstitutionofpartycompassespartyputinplace()themajorityofPartymembersandcadrestosethighstandardsandholdthebottomline,consciouslyabidebythe<code>and<rule>Oneistocontrolthe<standard>and<cases>,tightCloseconnectionwiththeirownthoughts,practicalworkandlife,effortstosolvetheproblems,toenhancethestudyandimplementoftheeffectivenessandpertinenceThesecondistoestablishahighstandardandholdthebottomline,consciouslyintheselfdisciplinepursuitofhighstandards,strictlyinthepartyawayfromtheredlinediscipline,discipline,abouttherulesandknowfear,distrust,theformationofthehonorsystem,complywiththesystem,safeguardsystemofgoodhabitsRegulationsanddisciplineregulationsof<<NewRevisionoftheCommunistPartyofChinacleanfingeredselfdisciplinecriterion>and<ChineseCommunistPartyDisciplinaryRegulations>isthePartyCentralCommitteeinthenewsituationtopromotethecomprehensivestrictlyrootofthelift,theregulationsofthepartyconstructionofkeepingpacewiththetimesWeshouldstudyandimplementtheStandards>and<>astheprimarypoliticaltask,adheretothepartyconstitutionduties,adheretothedisciplineof,JiYaninlaw,thefullimplementationofsupervisionanddisciplineaccountabilityresponsibilitiesforcoordinationandpromotion"fouroverall"strategiclayoutinXXDistrictvividpracticetoprovideastrongguaranteeSiJianWu,andeffectivelyenhancetheimplementationoftheimplementationofthe<code><>TheconsciousnessofGeneralSecretaryXipointedoutthatthepartyisinchargeoftheparty,tomanagethepartystrictly,itcancuregoodpartyCriterion>and<rule>keeppacewiththetimesisourpartytoformanewpotentialstrictlyrules,todeepenunderstandingoftherulinglaw,isacomprehensivestrictly,andstrengthenthesupervisionwithinthepartyimportantgrasperCriterion>closelylinkedtothethemeofselfdiscipline,selfdisciplineintensitymodulated,focusingonmorality,forthemajorityofPartymembersandcadressettosee,feelthehighstandard,showtheCommunistsnoblemoralsentimentDistrictOrdinance<<rule>theconstitutionofdisciplineintegrationintoapoliticaldiscipline,organizationanddiscipline,honestyanddiscipline,disciplineofthemasses,workdiscipline,discipline,emphasizediscipline,focusingonestablishedrules,todrawthepartyorganizationsandPartymembersdonottouchthebottomlinePartycommittees(party)toeffectivelystrengthenthestudyandpublicizetheimplementationofthe<code>and<rule>theorganizationandleadershipofcriterion>and<>afullrange,multiangle,deeppublicity,theformationofstudyandpublicizeandimplementtheboom,inordertoconsolidatethedevelopmentofgoodpoliticalenvironmenttocreateapositiveenvironmentandatmosphereThemajorityofPartymembersandcadrestostrictrequirements,the<rule>and<Ordinancecases>asaguidetoactionandbehaviorcriterion,adheretothemoralstandardsanddisciplineofthebottomline,tomaintainthedisciplineofworshipandawe,learning,compliance,andmaintainpartydisciplineandrulesofthemodelThedisciplineinspectionandsupervisionorgansandcadrestothe<code>and<>asthedeepeningofthe"three",andstrengthensupervisionanddisciplineofaccountabilityisimportanttofollowcorrectlygrasptheuseofsupervisionanddisciplineof"fourtypes",promotethecomprehensivestrictlyinnewrootsStrictdiscipline,adheretothedisciplineandrulesquiteinfrontoftheenterpriseintheimplementationofexpensivetoimplementtoexecuteThedisciplineinspectionandsupervisionorganstoimplementthe<code>and<Effortstoinvestigatecases>asanopportunity,adheretothepartyshouldmanagethepartystrictly,seriousperformanceoftheirdutiestopromotetworegulationsimplementationChangedisciplineconceptFromthesimple"investigationofillegal"toacomprehensive"stareatviolatediscipline"fromthebusinesscasetoprosecutethebigcasesandtimelysolvethesignsoftilttoFromtheorientationtothenormalsupervisionfromthetube"minority"toresistthe"most"GuidePartymembersandcadrestoseriouslyimplementthe<code>and<rule>,consciouslyabidebythepolitical,organizational,honestpeople,work,lifesixdisciplineUrgetheleadershipcadressenttoplayanexemplaryrole,taketheleadinstrictlyenforcedRelaxationandrestStrongwindisSuJi,closelylinkedtothe"fourwinds"pronetomultiple,themassesreflectthestrongimportantnodesand,gluedtothefourwinds"newform,newtrends,seriouslyinvestigateanddealwithviolationsofthecentraleightprovisionsofthespirit,toincreasethebulletinexposureintensity,theformationofChajiu"fourwinds"loudly,continuetoreleaseanddisciplinemustbestrictsignalAtthesametime,extendedsupervisiontentacles,throughthedevelopmentoftheruralandfisherypartyconductLianzhengconstructioninspection,issuedinatimelymanner,Chajiuoccurredingrassrootssideofcorruptionandunhealthy,andearnestlysafeguardtheinterestsofthemassesandsocialstabilityThecreativityanddisciplineGraspandmakegooduseofthesupervisionanddisciplineof"fourtypes",toensurethePromotingcluestolotsofdisciplineandthelawofthevacuumtube,stricttogetherNotonlytothe"less"and"veryfew"thoroughinvestigationseverelypunished,butalsothe"most"tomaintainzerotolerancetrendthroughlayersofconductivepressure,letthedisciplineabouttherulesforeachpartymembersandcadresconsciouslyfollowAtpresent,itisnecessarytoimplementthe"list"management,strictlyfollowthecluestothedisposaloffivestandards,maketheclassificationofdisposal,dynamiccleanupZadokPartycommitteesatalllevelstoimplementthemainresponsibility,comprehensiveuseofdisciplinaryactionandtissueprocessingandothermeanstoeffectivelycurbthecommonplace,usedtoseedonotblamethe"smallproblem",notbecauseof"practice"and"exception"ProminentDisciplinecharacteristics,theproblemsofviolationofdisciplineandrulesintothefocusofsupervisionanddisciplineanddisciplinaryreviewAtthesametime,increasecasedoublechecktheintensity,theseriousproblemsofdisciplineviolationsor"fourwinds"banbutnotabsolutely,notonlytobehelddirectlyresponsible,butalsoheldleadershipresponsibilitynotonlytopursuestudiesthemainresponsibilityofthePartycommittee,andtopursueCommissionforDisciplineInspectionandsupervisionresponsibilitiesandpromoteaccountabilitytobecomethenewnormTheimplementationofsupervisoryresponsibilityMaintain<code>and<rule>theseriousnessandauthorityofthedisciplineandrulesandtrulybecometheparty'srulerDisciplineassupervisionwithinthepartythespecializedagency,wemuststrengthentheresponsibilitytoact,adheretotheImpartialdisciplineaccountability,earnestlywillbestrictdiscipline,disciplinemustbepunished,andseverelypunishtheactsinviolationofrulesandregulation
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