CHAPTER 10. DIFFERENTIAL EQUATIONS
λN=α+βáI=λO=α−βáI=ïÜÉêÉ==
O
é
α=− I=
O
Qè−éO
β= I==
íÜÉå=íÜÉ=ÖÉåÉê~ä=ëçäìíáçå=áë==
ó=Éαñ()`NÅçëβñ+`Oëáåβñ K==
=
fåÜçãçÖÉåÉçìë=iáåÉ~ê=bèì~íáçåë=ïáíÜ=
çåëí~åí=======================
çÉÑÑáÅáÉåíë==
ó′′+éó′+èó=Ñ(ñ)K==
qÜÉ=ÖÉåÉê~ä=ëçäìíáçå=áë=ÖáîÉå=Äó==
ó=óé+óÜI=ïÜÉêÉ==
ó =áë==~=é~êíáÅìä~ê==ëçäìíáçå=çÑ==íÜÉ=áåÜçãçÖÉåÉçìë=Éèì~íáçå=é
~åÇ=óÜ=áë=íÜÉ=ÖÉåÉê~ä=ëçäìíáçå=çÑ=íÜÉ=~ëëçÅá~íÉÇ=ÜçãçÖÉåÉ-
çìë=Éèì~íáçå=EëÉÉ=íÜÉ=éêÉîáçìë=íçéáÅ=NNTPFK=
fÑ=íÜÉ=êáÖÜí=ëáÇÉ=Ü~ë=íÜÉ=Ñçêã==
Ñ()ñ =Éαñ()mN()ñÅçëβñ+mN(ñ)ëáåβñ I==
íÜÉå=íÜÉ==é~êíáÅìä~ê=ëçäìíáçå=ó =áë=ÖáîÉå=Äó==é
óé=ñâÉαñ()oN()ñÅçëβñ+oO(ñ)ëáåβñ I==
ïÜÉêÉ=íÜÉ=éçäóåçãá~äë=oN(ñ)=~åÇ=oO(ñ)=Ü~îÉ=íç=ÄÉ=ÑçìåÇ=
Äó=ìëáåÖ=íÜÉ=ãÉíÜçÇ=çÑ=ìåÇÉíÉêãáåÉÇ=ÅçÉÑÑáÅáÉåíëK==
- fÑ=α+βá=áë=åçí=~=êççí=çÑ=íÜÉ=ÅÜ~ê~ÅíÉêáëíáÅ=Éèì~íáçåI=íÜÉå=
íÜÉ=éçïÉê=â=MI= - fÑ=α+βá=áë=~=ëáãéäÉ=êççíI=íÜÉå=â=NI=
fÑ=α+βá=áë=~=ÇçìÄäÉ=êççíI=íÜÉå= Oâ= K==
- aáÑÑÉêÉåíá~ä=bèì~íáçåë=ïáíÜ=ó=jáëëáåÖ=
ó′′=Ñ()ñIó′K==
pÉí= óì= ′K=qÜÉå=íÜÉ=åÉï=Éèì~íáçå=ë~íáëÑáÉÇ=Äó=î=áë==
ì′=Ñ()ñIìI==
ïÜáÅÜ=áë=~=Ñáêëí=çêÇÉê=ÇáÑÑÉêÉåíá~ä=Éèì~íáçåK=