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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 17H2 ;jh fBy/VB ;wheoD (Exact Differential Equations)

fBy/VB ;wheoD M dx + N dy = 0 ;jh (exact) j't/rh i/eo j'D. i/eo fdZsk

j'fJnk ;wheoD ;jh j? sK n;hA fJ;d/ pknd fBwB fbys edw T[mktKr/^
(i) M B{z x d/ ;zdoG ftZu nB[ebB eoKr/ id'A fe y ;fEo j'D.
(ii) N B{z e/tb y d/ ;zdoG ftZu nB[ebB eoKr/ ns/ n;hA e/tb T[jBK gdK dk jh nB[ebB
eoKr/ fi; ftZu x Bk j'D.
(iii) T[go'es d'jK nB[bBK dk :'r eo btKr/.
fJ; soQK i/eo fBy/VB ;wheoD M dx + N dy = 0 ;jh (exact) j? sK fJ;dk jZb fBwB fbus
j't/rk^

(y B{z ;fEo wzBd/ j'J/) O (e/tb T[jBK d' dk fi; ftZu x Bk j't/) = c
2
2
T[dkjoD ti'L (x – ay) dx – (ax – y ) dy = 0 dk jZb gsk eo'.
2
2
fJZE/, M = x – ay ns/ N = (ax – y ) jB.
ns/

fJ; soQK j?, fJ; bJh fdZsh j'Jh ;wheoD ;jh (exact) j?.

j[D (y B{z ;fEo wzBd/ j'J/) HHH(1)

ns/ (e/tb T[j gd fi; ftZu x Bk j'D)

∴ ;kB{z T[gbpX j't/rk^
(i) + (ii) = c (ekbgfBe ;fEo nze)
iK

iK

Nk;e dk jZb eZY'. (T[Zso L )

;t?^w[bKeD (Self Assessment)

1H ykbh ;EkBK dh g{osh eo' (Fill in the blanks)^
1H fBy/VB ;wheoD T[j ;wheoD j[zdh j? fi; ftZu HHHHHHHHHH ns/ ;[szso ubokPhnK
j[zdhnK jB.
2H e'Jh th ;wheoD o/yh ejkJ/rk id'Afe nkPfos ubokPhnK d/ HHHHHHHHH gfjb/ e'Nh d/
j'D.

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