Page 308 - 1300 Math Formulas

CHAPTER 10. DIFFERENTIAL EQUATIONS

1172. mçéìä~íáçå=aóå~ãáÅë=EiçÖáëíáÅ=jçÇÉäF=
Çm  m 
= âm  −N  I==
Çí  j 
ïÜÉêÉ= () ím =áë=éçéìä~íáçå=~í=íáãÉ=íI=â=áë=~=éçëáíáîÉ=Åçåëí~åíI=
j=áë=~=äáãáíáåÖ=ëáòÉ=Ñçê=íÜÉ=éçéìä~íáçåK==
=
qÜÉ=ëçäìíáçå=çÑ=íÜÉ=ÇáÑÑÉêÉåíá~ä=Éèì~íáçå=áë==
m () í = jm M − âí I=ïÜÉêÉ=m = m ( ) M =áë=íÜÉ=áåáíá~ä=éçéì-
M
M ( m + m M )j − É
ä~íáçå=~í=íáãÉ=í = K===
M
=
=
=
10.2 Second Order Ordinary Differential
Equations

=
1173. eçãçÖÉåÉçìë=iáåÉ~ê=bèì~íáçåë=ïáíÜ=`çåëí~åí=`çÉÑÑáÅáÉåíë==
ó + ′′ ó é + ′ èó = M K==
qÜÉ=ÅÜ~ê~ÅíÉêáëíáÅ=Éèì~íáçå=áë==
λ O + é +λ è = M K==
=
fÑ= λ =~åÇ= λ =~êÉ=ÇáëíáåÅí= êÉ~ä=êççíë= çÑ=íÜÉ=ÅÜ~ê~ÅíÉêáëíáÅ=
O
N
Éèì~íáçåI=íÜÉå=íÜÉ=ÖÉåÉê~ä=ëçäìíáçå=áë==
ó = ` N É N λ ñ + ` O É O λ ñ I=ïÜÉêÉ==
` =~åÇ=` =~êÉ=áåíÉÖê~íáçå=Åçåëí~åíëK==
O
N
==
é
fÑ=λ = λ = − I=íÜÉå=íÜÉ=ÖÉåÉê~ä=ëçäìíáçå=áë==
N
O
O
é ñ
−
ó = ( N ` O ñ )` + É O K==
=
fÑ=λ =~åÇ=λ =~êÉ=ÅçãéäÉñ=åìãÄÉêëW=
N
O

298