Page 293 - DECO403_MATHEMATICS_FOR_ECONOMISTS_HINDI

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

bdkbZ vodyu lehdj.kksa dk ifjp; vkSj gy % pyjkf'k;ksa dh i`FkDdj.kh; n'kk ,oa le:i lehdj.k

1 dy uksV
, .k - tgk¡ % ,d fLFkjkad gSA
f () ydx

vr% lehdj.k (2) dks vc ge fuEufyf[kr :i esa fy[k ldrs gSaµ
1 dv + Pv ,
kdx

dv
;k , % " , % tks fd ,d js[kh; lehdj.k gSA
dx
dy 1 2 6
mnkgj.k 5 % + y = xy dk gy fudkfy,A
dx x

fn;s gq, lehdj.k dks ls Hkkx nsus ij
1 dy + 1 1
.
y 6 dx x y 5 ,

1 dv 5 dy
ekuk 5 = v , −
y dx y 6 dx
1 dy 1 dy
;k , −
y 6 dx 5 dx
lehdj.k (1) esa j[kus ij
1 dv 1 dv 1
− + v , x 2 − v = − 5x 2
5 dx x dx 5
;g ,d js[kh; lehdj.k gS ftlesa " ,d vkfJr pyjkf'k gSA
;gk¡ , 2 'C rFkk , 2 '

∫ Pdx =   ∫ − 5  dx , − 5 log x = log x = 5 log  1 
vr%  x     x  5 

∴ e ∫ P dx , e log (1/5) = x 1 5

" * , ∫ Q (I.F.) dx + c

−
;k " C , ∫ − 5x 2 (1/ x 5 ) dx + c , 5 x dx + ∫ − 3 c
 1   1  5  1 
 5   5  , −  2  + c [ v = 1/ y 5 ]
 y   x  2 x  

1 5 1  
;k 5 5 +  2  + c
xy 2 x  

;gh vodyu lehdj.k dk gy gSA