Page 127 - Math Grade 12 (Advance)

PROEUS DARA
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tij{j fil~'2 tel~ ti tti5Hl5 rn & S fH bl.hfl1Jg 2 1h H-J f ti5 S Si:l'tflS t'i:HHt.fl tl ~ 'tflS nb IH 9i:
U UU I U
f!) r.;l Q1 «:» C\ 0 C\
y"+by'+cy = p(x) tt:Jru p(x) dlHS?l'i:3S'tH15:&hlt'lhlS~ m1ru b sb c dlussmHt'l~ '1
I IJ I U U IJ

... .,
:unuun.n : n:iHLMtlihl'i§fil~ y"- y = 2x (E) '1
s. ~ C» 012 eJ
tU"MW: hl'i§fil~ y"-y = 0 'tfl2hl'i:3fil~hlmru A -1 = 0 tt:Jru'tflS'ghl A = 1 ,
1
l = -1
2
.,
hl'i§fil~ (E) HluhlHhl~dl: (y'-y)'+(y'-y) = 2x

mh z = y' - y : Z' + z = 2x ( 1 )

tq'litL'i§'li~ru~~S&tl~ A : Z = A(x)e-x =::} Z' = A'(x)e-x
IJ

A'(x)e-x = 2x Y. A'(x) = 2xex

A(x) = J2xe-xdx = 2(x-1)e''+B

t:Jutsg Z = [2(x 1)ex+B]e-x = 2(x-1)+Be-x
u
&L:fltliZ=y'-y: y' y=2(x-I)+Be-x (2)

Ctt Ql X
M'i§fil~ y'- y = o 'tfl2ut~ru y = Ce
tq'litL'i§'li~ru~~Sttl~ C : y = C(x)ex , y' = C'(x)e'' + C(x)ex
IJ

C'(x)ex = 2(x-1) +Be-x

-x -2x
C'(x) = 2(x-l)e +Be
2
C(x) = 2J(x l)e-xdx+Bfe- xdx= -2xe-x-~e- x+C 1
2
( C2 = ~)

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