Page 263 - DECO403_MATHEMATICS_FOR_ECONOMISTS_PUNJABI

VED1
E L-LOVELY-H math17-1 IInd 21-10-11 IIrd 21-10-12 IVth 21-4-12 Vth 20-8-12

Tanima Dutta, LPU fJekJh^17 L fBy/VB ;wheoDK dh ikDekoh ns/ jZb L ubokPhnK dh gqEeDh dPk ns/ ;wo{g ;wheoD

fJekJh^17L fBy/VB ;wheoDK dh ikDekoh ns/ jZbL B'N

ubokPhnK dh gqEeDh dPk ns/ ;wo{g ;wheoD
(Introduction to Differential Equations and Solutions:
Variable Separable Case and Homogenous Equation)

ftP/ t;s{ (Contents)
T[d/P (Objectives)

gq;sktBk (Introduction)
17H1 gfjbk eqw ns/ gfjbh e'Nh dk fBy/VB ;wheoD
(Differential Equation of First Order and First Degree)
17H2 ;jh fBy/VB ;wheoD (Exact Differential Equations)
17H3 ;koKP (Summary)

17H4 Ppde'P (Keywords)
17H5 nfGnk; gqPB (Review Questions)
17H6 ;zdoG g[;seK (Further Readings)

T[d/P (Objectives)

fJ; fJekJh d/ nfXn?B s'A pknd ftfdnkoEh :'r j'Dr/L

• gfjb/ eqw ns/ gfjbh e'Nh d/ fBy/VB ;wheoD s'A ikD{ j'Dr/.
• ;jh fBy/VB ;wheoD s'A ikD{ eokT[Dk.

gq;sktBk (Introduction)
fBy/VB ;wheoD T[j ;wheoD j[zdh j? fi; ftZu nkPfos ns/ ;[szso ub okPhnK j[zdhnK jB
ns/ nkPfos ub okPhnK d/ fJZE iK fJZe s'A tZX ;[szso ub okPhnK d/ ;kg/y ftZu ftfGzB r[DKe
(derivatives) j[zd/ jB. fJZe fBy/VB ;wheoD dk eqw (order) T[; ;wheoD ftZu Pkfwb ftfGzB
r[DkeK dk T[Zusw eqw (highest order) j[zdk j?. e'Jh th ;wheoD o/yh ejkJ/rk id'A fe nkPfos
ub okPhnK d/ r[DKe gfjbh e'Nh d/ j'D, BjhA sK T[j r?o^o/yh ejkT[Dr/.
cbB f (x) ftfGzB ;wheoDK dk jZb ejkJ/rk id'A fe fJ;B{z fe;h ;wheoD ftZu gqfs;Ekfgs eoB
sK fJj ;wheoD B{z fJZe fJekJh (identy) sZe xZN eo fdzdk j? ns/ ;ko/ jZbK d/ eZYD dh
gqfefonk B{z fBy/VB ;wheoD dk jZb ejkJ/rk.
;XkoD jZbL fJZe fBy/VB ;wheoD dk jZb fi; ftZu ;[szso ekbgfBe ;fEo nze fBy/VB
;wheoD d/ eqw d/ pokpo j'D sK T[;B{z T[;dk ;XkoD jZb fejk iKdk j?.
ftP/P jZb (Particular Solution)L ;XkoD jZb ftZu ;fEo nzeK B{z i/eo e'Jh ftP/P w[Zb fdZsk
iKdk j? sK T[j T[; ;wheoD dk ftP/P jZb fejk iKdk j?.
x
x
T[dkjoD ti'AL y = Ae + B/e teo B{z A ns/ B d/ ftfGzB w[ZbK d/ bJh fBy/VB ;wheoD gsk
eo'.
x
x
fdZsk j'fJnk w[Zb y = Ae + B/e HHHH(1)

LOVELY PROFESSIONAL UNIVERSITY 257