Page 101 - Math Grade 12 (Advance)

PROEUS DARA
y-1 = xy' ~ xy'-y = -1 ctltU~AlJ~tt:fiiH'MJf.l5CSUinnm~~ y =ex+ 1
\J
""'
., tU'eAlJ xy ' -y = -1 ffiutUHt\5~: xy' = y-1
1
- - · ddy = l mM~m~~u:l~~~Mtrnrn!:hti9 1 t'E:lrnffiutmn~Hl:l~ms '1
y- 1 X X eJ ~

§wgsw: M~ma~ta~~t'MJrnrn!:hti9 1 t'E:lrnffiutf!JnHtl:l~ms mM~AlJ

t'E:lrntunrunM~rnam:ns&~L-e~~t9i g(y) ~~ = f(x) '1
\J

3. nuJmitl:uunnrutJmt g(y) ~~ = J<x)

""' 2 3
t!:hgLnJltl5tU'eAl~ y' = X y
2
tUfW : y' = il ffiutUHtUJctl ~ dy = x
y dx
_!_ dy = i i1 §1 dy = i dx
l dx tJ /
2
tqffi~tfiLAlrntruH~il~n~ts d~ = x dx tf:lQlS
y
J d; = j/dx
y
1 1 3 o a
- - = -x +c (c ctluSStdHlm'etl5fiQlS)
1.1 1.1
2/ 3
2 3 2 2
3 x y + 2cy + 1 = 0
2
~ 2i/ + 6c/ + 3 = 0 mm~ru~t9its tU~Al~~td~~ ttUJffi y' = x l '1
tneufl : t~-ej t!:h g1f5ltl5 t\5~ Al~~ td~ ~ ~ tUJ f.l5 rn !:hUg 1 ~E:l ffiffiu tQJ fiH td J QlS

&?llJil :
IJ
- MHM~M~Al~2Jt9ictln~ g(y) ~~ = f(x)

tqffi~tfiunrncruH~il~ 2 tuJus~HtdJ x
o a
J g(y)dy = J f(x)dx G(y) = F(x) + c (c ctluSStdHliTl'etl5fiQlS)
1.1 1.1
C» Q}c.J "':, c'
ttlrn G(y) ctlLn~9~tSH~f:l'e~ g(y) s~ F(x) dl1Jl"e91tSH~f:l'eS f(x) '1

Wtmzftf.f : fi~thrun-etU~Al~~~tUAl"e t~tU'i§AliruTI!Hftlf.l5ffiutmnHtdJQlS ?
Ill' c:; 6'IJ "'
1
fi. dy = 2x(y + 1) 2. dy = ~ + ~ R. dy = ln(xy) '115. ddxy = ex+ Y '1
dx y dx x y dx
t!:hg1nnruM~AlifE:lrnffiut'mnHtd~ms m-ernn2nJH~-e y(2) = o '1
Li ~ 9 Ill

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