解一阶常微分方程范文

在当今的科学发展飞速的新时代，越来越多的高科技开始运用于我们的学习、工作和生活当中。科技，已成为我们走向高质量生活的一座桥梁，一根绳梯。ofvision.3,build,fittinginwiththeurbanmasterplaninYibincityrapidrailtransitlongtermnetwork,aswellasthevisionofYibincity,andfuturedevelopmentofrailtransitnetwork.4,Yibincity,preliminaryrailtrafficlevelsservicelevels,systemmodel,andtechnicalstandards.5,toensurethatnetworkcanbeimplemented.6,stableconditionsforplanningandsupportingofYibincitytracktrafficconstructionandformationofrailtransitindustry,provideconditionsforthestart-upanddevelopmentofrailtransitinYibincity.1.7technicalcoursetechnologyistheproject'sresearchprogramandresearchideas.Technologyreflectsthevariousstagesintheprocess,logicalrelationsbetweenvariouslevels,research,techniquesandphases.Networkplanningprocessthewholeprocesscanbedividedintofourparts,namely,backgroundresearch,networkarchitectureresearch,planningandimplementationofresearchandprogramminginterfaces.Figure1.7-1Yibincityrailtransitnetworkplanningtechnologyroadmapplanninginterfaceismainlyresponsiblefornetworkplanninginterfacewithfollow-upplanningtasks.NetworkplanningUrbanplanningsysteminatransitionalposition,onlinenetworkplanningiscompleted,willbecarriedoutassoonaspossiblethefollowingplanningprojects:1,detailedcontrolofthelandofrapidrailtransitnetworkplanning;2,thepartitioningfornetworkplanning;3,jointplanningofrailtransportandurbantransportinotherways;Detailedtechnicalcoursesseebelow.Figure1.7-2Generaltechnologyroutefigure2ndchapterCitystatusanddevelopmentplanning2.1citybasicprofile2.1.1解一阶常微分方程1.知识准备1.1变量分离方程形如()()dyfxydx(1)的方程，称为变量分离方程，()fx，()y分别是x，y的连续函数.这是一类最简单的一阶函数．如果()0y，我们可将(1)改写成()()dyfxdxy，这样变量就分离开来了.两边积分，得到()()dyfxdxcy，c为任意常数．由该式所确定的函数关系式(,)yyxc就是常微分方程(1)的解．1.2积分因子恰当微分方程可以通过积分求出它的通解．因此能否将一个非恰当微分方程化为恰当微分方程就有很大的意义．积分因子就是为了解决这个问题引进的概念．如果存在连续可微函数,0xy，使得,,,,0xyMxydxxyNxydy为一恰当微分方程，即存在函数u，使MdxNdydu，则称,xy为方程,,0MxydxNxydy的积分因子．函数,xy为,,0MxydxNxydy积分因子的充要条件是()()MNyx，即在当今的科学发展飞速的新时代，越来越多的高科技开始运用于我们的学习、工作和生活当中。科技，已成为我们走向高质量生活的一座桥梁，一根绳梯。ofvision.3,build,fittinginwiththeurbanmasterplaninYibincityrapidrailtransitlongtermnetwork,aswellasthevisionofYibincity,andfuturedevelopmentofrailtransitnetwork.4,Yibincity,preliminaryrailtrafficlevelsservicelevels,systemmodel,andtechnicalstandards.5,toensurethatnetworkcanbeimplemented.6,stableconditionsforplanningandsupportingofYibincitytracktrafficconstructionandformationofrailtransitindustry,provideconditionsforthestart-upanddevelopmentofrailtransitinYibincity.1.7technicalcoursetechnologyistheproject'sresearchprogramandresearchideas.Technologyreflectsthevariousstagesintheprocess,logicalrelationsbetweenvariouslevels,research,techniquesandphases.Networkplanningprocessthewholeprocesscanbedividedintofourparts,namely,backgroundresearch,networkarchitectureresearch,planningandimplementationofresearchandprogramminginterfaces.Figure1.7-1Yibincityrailtransitnetworkplanningtechnologyroadmapplanninginterfaceismainlyresponsiblefornetworkplanninginterfacewithfollow-upplanningtasks.NetworkplanningUrbanplanningsysteminatransitionalposition,onlinenetworkplanningiscompleted,willbecarriedoutassoonaspossiblethefollowingplanningprojects:1,detailedcontrolofthelandofrapidrailtransitnetworkplanning;2,thepartitioningfornetworkplanning;3,jointplanningofrailtransportandurbantransportinotherways;Detailedtechnicalcoursesseebelow.Figure1.7-2Generaltechnologyroutefigure2ndchapterCitystatusanddevelopmentplanning2.1citybasicprofile2.1.1-2-()MNNMxyyx．假设原方程存在只与x有关的积分因子x，则0x，则为原方程的积分因子的充要条件是()MNxyx，即()MNyxxN仅是关于x的函数．此时可求得原方程的一个积分因子为xdxe．同样有只与y有关的积分因子的充要条件是()MNyxyM是仅为y的函数，此时可求得方程(11)的一个积分因子为ydye1.3恰当微分方程考虑微分形式的一阶微分方程,,0MxydxNxydy(11)，如果该式的左端恰好是某个二元函数,uxy的全微分，即,,,uuMxydxNxydyduxydxdyxy则称(11)为恰当微分方程．对于一阶微分方程,,0MxydxNxydy，若有MNyx，则该方程必为恰当微分方程．我们接着讨论如何求得该恰当微分方程的解．我们可以把,uMxyx看作只关于自变量x的函数，对它积分可得,uMxydxy，由此式可得,dyuMxydxxxdy，又因为有,uNxyx，故在当今的科学发展飞速的新时代，越来越多的高科技开始运用于我们的学习、工作和生活当中。科技，已成为我们走向高质量生活的一座桥梁，一根绳梯。ofvision.3,build,fittinginwiththeurbanmasterplaninYibincityrapidrailtransitlongtermnetwork,aswellasthevisionofYibincity,andfuturedevelopmentofrailtransitnetwork.4,Yibincity,preliminaryrailtrafficlevelsservicelevels,systemmodel,andtechnicalstandards.5,toensurethatnetworkcanbeimplemented.6,stableconditionsforplanningandsupportingofYibincitytracktrafficconstructionandformationofrailtransitindustry,provideconditionsforthestart-upanddevelopmentofrailtransitinYibincity.1.7technicalcoursetechnologyistheproject'sresearchprogramandresearchideas.Technologyreflectsthevariousstagesintheprocess,logicalrelationsbetweenvariouslevels,research,techniquesandphases.Networkplanningprocessthewholeprocesscanbedividedintofourparts,namely,backgroundresearch,networkarchitectureresearch,planningandimplementationofresearchandprogramminginterfaces.Figure1.7-1Yibincityrailtransitnetworkplanningtechnologyroadmapplanninginterfaceismainlyresponsiblefornetworkplanninginterfacewithfol