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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

3H fJZe fBy/VB ;wheoD dk jZb fi; ftZu ;[szso ekbgfBe ;fEo nze fBy/VB ;wheoD B'N
d/ eqw d/ pokpo j't/ sK T[;B{z T[;dk HHHHHHHHHHHH jZb fejk iKdk j?.
4H ;XkoD jZb ftZu ;fEo nzeK B{z i/eo e'Nh ftP/P w[Zb fdZsk iKdk j? sK T[j T[; ;wheoD
dk HHHHHHHHHHH jZb fejk iKdk j?.
dy f (, )
xy
5H i/eo fJZe fBy/VB ;wheoD = 1 d/ o{g ftZu gqdofPs ehsk ikt/ sK T[j
x
y
dx f 2 (, )
HHHHHHHHHHH ;wheoD ejkT[Adh j?.

17H3 ;koKP (Summary)
• fBy/VB ;wheoD T[j ;wheoD j[zdh j? fi; ftZu nkPfos ns/ ;[szso ubokPhnK j[zdhnK
jB ns/ nkPfos ubokPhnK d/ fJZe iK fJZe s'A tZX ;[szso ubokPhnK 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[Zuso eqw (highest order) j[zdk j?. e'Jh th ;wheoD o/yh
ejkJ/rk id'A fe nkPfos ubokPhnK d/ r[DKe gfjbh e'Nh d/ j'D, BjhA sK T[j r?o^o/yh
ejkT[Dr/.

• ;XkoD jZb L 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 ;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?.
• i/eo fBy/VB ;wheoD fBwBfbys o{g ftZu gqdofPs j't/^

f 1 (x) dx = f 2 (y) dy
fJZE/ f 1 (x) ns/ f 2 (y) eqw nB[;ko x ns/ y d/ cbB jB.
• nfijh dPk ftZu ;wheoD d/ d'jK gk;/ nB[ebB eo b?Ad/ jB ns/ T[; s'A pknd ;wheoD
d/ fJZe gk;/ e'Jh ekbgfBe ;fEo nze i'V b?Ad/ jB.

17H4 Ppde'P (Keywords)

• ;wo{g (Homogeneous) ^ ;wKrh.
• gqEeheoD (Separable) ^ tZy^tZy.

17H5 nfGnk; gqPB (Review Questions)

x
x
1H y = A e + B/e teo B{z A ns/ B d/ ftfGzB w{bK d/ bJh fBy/VB ;wheoD gsk eo'.
2
dy
(T[Zso L = y )
dx 2
 x   y 
2
c
2H   dx =− 1  dy dk jZb eZY'. (T[Zso L 1 + 2 1 x + + y = )
 1 + 2   1 x  + y  
2
dy
x2
−
3H + 2xy e − x 2 dk jZb eZY'. (T[Zso L ye = x + c)
dx

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