Page 121 - Math Grade 12 (Advance)

PROEUS DARA
r ..,._,.., 0 ( ) -4x 0 l': , 1 -4x -4x
• ,., o '"' y = c 2 x e Sl '\} y = c (x)e - 4c (x)e
2
2
4 4
1 2
C (x)e- x-4c (x)e-4x+4c e- '' = c e x
2 2 2 1
1 ( ) -4x 2_,
c x e = c e
2
1
6x cl 6x 6x
J
c 2 ( x) = c e dx = e + A = Be + A
1
6
v., r 0 0 (B 6x + A) -4x A -4x B 2x
~"'""'o y = e e = e + e

-4x 2x
y = Ae +Be
"
'
MfilflJ:
-4x 2x ..,.... "" r.4"' ""
'"y = Ae +Be wl1:3t'i:Hti9&l:ti&Sf15'i:Hm y"+2y'-8y = 0 (E)
"" u
-4x "'14 2x • .-.4..,.... "" "' ""
"'y = e Sw y = e tullut1:3t~t15tffHl.HSfU'i§ffU y"+2y'-8y = 0
1
2
Ql 0 Q. l"'f'4 Ql Q:l Q. ~
tLm8tlH?'id~M y 1 , y' 1 sb y" 1 &i::iigbM'i5fm (E) t?'isbrnsM'i5.ffltH16'i t'Ulru
1
ttlt?'in~M y , y' Sb y" gbfU~nU (E) t?ifh:nsM'i5.ffltl~6'ittl~ '1
2 2 2
1

Q)QI 0. 0 Q Q
- &tifU'i§ffl~Mfflru'HlSYM 2 ctl1:3~St16'itdJb~ A- = a sb A- 2 = ~ tS'H
1
fU~ffl~ y"+by'+cy = 0 't:f1Sljt~ti59tlll y = Aeax+Bepx ttlru A Sb B
"" u
0 ..
ctl1:3S StGHUll'i5t15nQIS
1J 1J

' 0
{lJfJTJ lttfJ:
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n. ti:t18UlflruM~m~~td~citMJru y" + yl -2y = o (E) '1

I 0 Ql tUQpeJ tO
ffl6'iffi'i51:Hlfl1:3 (x = 0 , y = l) t'Ult15't5Sl6'i'iHSbt~HfflbH'lb1:3rul1:3
1 c: 'If LJ 1
9
tSl8'HlSt'i5 n.nLrnli9Mt~sb 4 '1 Mcit~JtfflbtSl8 '1

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