Page 268 - DECO403_MATHEMATICS_FOR_ECONOMISTS_PUNJABI

VED1
E L-LOVELY-H math17-1 IInd 6-8-11 IIrd 21-10-12 IVth 21-4-12 Vth 20-8-12

noEPk;soh dk rfDs

B'N dy 2
T[dkjoD L 5 + 2xy e − x dk jZb eZY'.
−
dx
dy
T[go'es ;wheoD dh + PY = Q Bkb s[bBk eoB s/ n;hA d/yd/ jK
dx
P = 2,xQ = e − x 2
d'jK dk gqEe^gqEe ‘x’ d/ ;kg/y nB[ebB eoB s/

fJ; soQK e ∫ p dx = e x 2

fdZs/ j'J/ fBy/VB ;wheoD dk jZb j't/rk^

iK
17H1H5 o/yh o{g ftZu pdbDk (Change in Linear Form)

i/eo e'Jh fBy/VB ;wheoD o/yh o{g ftZu pdbh ik ;edh j? sK T[;dk jZb d' ftXhnK d[nkok
ehsk ik ;edk j?^
(I) poB'bh ;wheoDL i/eo e'Jh ;wheoD fBwB fbus o{g ftZu fdZsk j'fJnk j't/^

dy
n
+ PY = Q y
dx
-n
sK nfijh dPk ftZu n;hA d'jK gk;/ y Bkb r[Dk eod/ jK.
n
y − n dy + PY −+ 1 = Q HHH(1)
dx
dv n dy
−
n
)
n;hA y −+ 1 = v oZy fdzd/ jK sK (1 ny − j't/rk.
dx dx
j[D ;wheoD (1) dk o{g j/m nB[;ko j't/rk^
1 dv
+ pv = Q
−
1 n dx
dv
−
iK + (1 n pv = (1 n )Q HHH(2)
−
)
dx
fJj ;wheoD fJZe o/yh ;wheoD j?, fiZE/ v fJZe nkPfos ubokPh j?. fJ; fBy/VB ;wheoD
dk jZb 17H1H4 d/ nB[;ko j't/rk.
(II) i/eo e'Jh ;wheoD fBwB fbus o{g ftZu gqdofPs j't/^
dv
φ
+ P ( ) = Q f ( )
y
y
dx
fiZE/, P ns/ Q e/tb x d/ cbB j?.

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