Page 115 - Math Grade 12 (Advance)

PROEUS DARA

Ql ~ II I C) 0 I Q1
W'i:Hm ~ t d ~ ~ t WJ bl.Hli t:ll'U 9 1 1:ll S fltl ~ t 9i

G ddy = f(x) 'i:llStH~ rug & 9i y = Jf(x)dx + c
X ~ U
o g(y)ddy = f(x) 1:llStH~ti59t9i G(y) = F(x)+c tt:lru G(y) = Jg(y)dy
X N u
dy "" n4 -ar 0
.. y'+ay = o 'i5 -+ay = 0 1:llStH'\3ti59tlfl y = Ae, (A rtltiSStdn
"' dx "" u u

1. nfHUtJlti5W~fm2&n~~twJru

,
n. y 2 2 1 2. y = e -2x
~ ' = x -x+
_ , 2x X o • c:.~
1=1.)' = -2- ill. y' = - - f'Hl..flfitru ( - 1, I )
2
x + 1 X - 1
""
0
'
tl. xy' = 1 fHl..flfitru ( o, + oo ) '1

2
n. ~ = cosx , y(~) = e 2. y' = e x , y(O) = 5
2
l='i. (3x -2)y' = 6x , y(l) = 4 ill. __i__ = I , y(O) = 0 '1
tanx
Ql: C» ll I C) ~ C)- 0 lt:/i
3. tt:iHLnllti5W'\3ffU~td~~tWJbtibtitStHrut:ll'i59 I
n. dy + 2y = o 2. 3dy + y = 0
dx dx
l='i. 2y'-3y = 0 ill. y'+yJi = o '1

4. tt:JlgLnnruw~nu'2tn~~t'wJrut1hsmrumti9 1 m'\3run2 n..n ttl ru§1
B S u
2. 2y' + y = 0 , y(ln4) = ~
n. - y' + 2y = o , y(3) = -2

4
l='i. 7y'+4y = 0 , y(7) = e- ill. 2y'-5y = 0 'y(l) = -3 '1

3
n. )' = X + ex , y' - )I = J - X 2. y = e x x- I , y' - 3 y = 3x + 2

l='i. y = sinx+ cosx , y' + y = 2cosx ill. y = x + lnx , xy' y = I lnx '1

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