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

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

a b B'N
fJZE/ ≠ dh ;fEsh j?, fJ; bJh x = X + h ns/ y = Y + k oZyD s/
a 1 b 1
−
+
−
DY (Y + k ) (X + h ) 1 Y − X + ( k h + 1)
= = HHHH(1)
)(X +
k h
DX (Y + k − h + Y − X + ( − + 5)
)5
k – h + 1 = 0 ns/ k + h + 5 = 0 oZyD s/ n;hA d/yd/ jK k = – 3, h = – 2k ns/ h dk wkB oZyD s/
;wheoD (1) j/m nB[;ko j't/rk^
dY Y − X
=
dX Y + X
Y = vX oZyD s/ n;hA d/yd/ jK

iK

d'jK gk;/ 2 Bkb r[Dk eoB s/
2 2v − 2v X
iK dv + dv =
v + 1 v + 1 dx
2
2
d'jK gk;/ nB[ebB eoB s/
–1
2
log (v + 1) = 2 tan v = –2 log X + c
–1
2
iK log (v + 1) + 2 log X = –2 tan v + c
2
–1
2
iK log [(v + 1) X ] = – 2 tan v + c
v dk wkB oZyD s/
2
–1
2
log (Y + X ) = – 2 tan (Y/X) = c
Y ns/ X dk wkB oZyD s/
2
2
–1
Log [(y + 3) + (x + 2) ] + 2 tan {(y + 3) / (x + 2)} = c
fJjh fdZs/ j'J/ nB[ebB ;wheoD dk jZb j?.
17H1H4 o/yh fBy/VB ;wheoD (Linear Differential Equation)
o/yh fBy/VB ;wheoD B{z fBwB fbys o{g ftZu gqdofPs ehsk iKdk j?^
dy
+ PY = Q
dx
fJZE/ P ns/ Q e/tb x d/ cbB j[zd/ jB ns/ y fJZe nkPfos ubokPh j?. fJ; ;wheoD dk jZB
eoB d/ bJh d'jK gk;/ e ∫ p dx Bkb r[Dk eoB s/

iK

d'jK gk;/ ‘x’ d/ ;zdoG ftZu nB[ebB eoB s/
∫ p dx ∫ p dx
+
ye = ∫ Q e dx c
fJjh ;kv/ fdZs/ j'J/ ;wheoD dk jZb j'J/rk.

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