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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

x
x
T[dkjD 2H (1 + e ) y dy = (1 + y) e dx dk jZb gsk eo'. B'N
jZb L fJ; ;wheoD B{z n;hA j/m nB[;ko th fby ;ed/ jK^

d'jK gk;/ fBy/VB eoB s/

iK

iK
x
y
iK c (1 + y) (1 + e ) = e fJjh T[go'es ;wheoD dk jZb j'J/rk.
17H1H2 ;wo{g ;wheoD (Homogeneous Equations)
i/eo fJZe fBy//VB ;wheoD d/ o{g ftZu gqdofPs ehsk ikt/ sK T[j ;wo{g

;wheoD ejkT[Adh j?. fJZE/ f 1 (x, y) ns/ f 2 (x, y); x ns/ y d/ ;wkB e'Nh d/ cbB jB. fJ; soQK
d/ ;wheoD B{z jZb eoB d/ bJh n;hA

oZy fdzd/ jK, fiZE/

nfijh ;fEsh ftZu fdZsk j'fJnk ;wheoD nZr/ fby/ o{g ftZu gqdofPs ehsk iKdk j?^

Gkt

fJZE/ ubokPhnK B{z gqEe ehsk ik ;edk j? ns/ T[; s'A pknd d'jK gk;/ T[jBK dk nB[ebB eo
b?Ad/ jK^

fJZE/, c fJZe ekbgfBe ;fEo w[Zb j?.

eh s[;hA ikDd/ j' ;wheoD dk nB[ebB eoB d/ pknd v d/ w[Zb d/ ;EkB s/ y/x oZy b?Ad/ jK
ns/ T[jh T[; ;wheoD dk jZb j'J/rk.

3
3
2
3
T[dkjoD 3H (x – 3xy ) = dx (y – 3x y) dy dk jZb gsk eo'.
fdZs/ j'J/ ;wheoD B{z j/m nB[;ko th fbfynk ik ;edk j?.
HHHH(1)

y = vx ns/ ;wheoD (1) ftZu oZyD s/

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