积分因子法的应用

:2003-10-27:2004-02-13:(1965-),,.:.(,350002):,.:;:O172.1:A:100627817(2004)0220269203ApplicationofintegrationfactormethodLIDe2xin(CollegeofComputerandInformation,FujianAgricultureandForestryUniversity,Fuzhou,Fujian350002,China)Abstract:Thefundamentalprincipleofintegrationfactormethodanditsapplicationtosomeequatityorineguatityprob2lemsweregiven.Keywords:integrationfactor;subsidiaryfunction,,[1,2].,11f(x),g(x)G(x),[f(x)eG(x)]=[f(x)+g(x)f(x)]eG(x),(1)F(x)=f(x)eG(x)[f(x)+g(x)f(x)]eG(x).R(x)=eG(x)f(x)+g(x)f(x).F(x)=f(x)eG(x)(2),.eG(x)0,:R(x)=eG(x)f(x)+g(x)f(x),F(x)=f(x)eG(x),(1)f(x)+g(x)f(x)0(0)F(x)0(0);(2)f(x)+g(x)f(x)0F(x)0;(3)f(N)+g(N)f(N)=0F(N)=0122.1f(x)+g(x)f(x)0(0)1f(x)[0,+),(0,+),f(0)=0,(0,+)f(x)-f(x),:(0,+)f(x)01f(x)0.f(x)-f(x),f(x)+f(x)0,f(x)+f(x)()332JournalofFujianAgricultureandForestryUniversity(NaturalScienceEdition)20046ex,F(x)=f(x)ex,F(x)0,(0,+)F(x)01F(x)=f(x)ex,x[0,+).(0,+)F(x)=[f(x)+f(x)]ex0.F(x)[0,+),F(x)[0,+),x(0,+)F(x)F(0)=0.ex0,(0,+)f(x)0.,f(x)g(x)[a,b],f(x)(a,b),f(a)0,(a,b)f(x)+g(x)f(x)0,(a,b)f(x)0.2.2f(x)+g(x)f(x)=02f(x)(0,+),f(1)=1,f(x)-2xf(x)=0,:(0,+)f(x)=x1f(x)=x.f(x)-2xf(x)=0f(x)-12xf(x)=0,f(x)-12xf(x)1x,F(x)=f(x)x,F(x)=0,(0,+)F(x)=11F(x)=f(x)x,x(0,+).(0,+)F(x)=f(x)x-f(x)12x(x)2=2xf(x)-f(x)2xx=0,,F(x)(0,+).F(1)=f(1)1=1,(0,+)F(x)=1,f(x)=x.,f(x)g(x)[a,b],f(x)(a,b),(a,b)f(x)+g(x)f(x)=0,[a,b]f(x)=Ce-G(x)[G(x)g(x),C].2.3f(N)+g(N)f(N)=03f(x)[1,2],(1,2),f(1)=2,f(2)=1,:(1,2)Nf(N)=-f(N)N1,f(N)=-f(N)N,f(N)+1Nf(N)=0.f(x)+1xf(x)x,F(x)=xf(x),F(N)=01F(x)=xf(x),x[1,2].F(x)[1,2],(1,2),F(1)=f(1)=2,F(2)=2f(2)=2.,(1,2)N,F(N)=0,f(N)+Nf(N)=0,f(N)=-f(N)N.,f(x)g(x)[a,b],f(x)(a,b),G(x)g(x),f(a)eG(a)=f(b)eG(b),(a,b)Nf(N)+g(N)f(N)=01,f(N)+g(N)f(N)=h(N),[3]F(x)=f(x)eG(x)-h(x)eG(x)dx,.2.4y(n)+g(x)y(n-1)=h(x)4y+2xy=2xe-x21072()33y+2xy,,ex2,1ex2,(yex2)=2x,yex2=x2+c.y=(x2+c)e-x2.,y+g(x)y=h(x),eG(x)[G(x)g(x)],[yeG(x)]=h(x)eG(x).yeG(x)=h(x)eG(x)dx,:y=e-G(x)[h(x)eG(x)dx](3)[2],(3)[2].,1,y(n)+g(x)y(n-1)=h(x),,(3),g(n-1)=e-G(x)[h(x)eG(x)dx],n-1.3f(x)+g(x)f(x),.:[1],,,.()[M].:,1983.173-177.[2].()[M].:,1996.342-344.[3].[J].,2003,6(3):31-33.(:)1722: