Page 120 - Math Grade 12 (Advance)

PROEUS DARA

meun:

• tU~fil~~ tt:lHHtUJrlHlhs n:irntJltig 2 y" +by'+ cy = o h!lut'DHhlH:h hl~fil2

(y'-ay)'-p(y'-ay) = 0 &'tlrn a Sti ~ r:hyhltShl~fllahlfflru

2
A + b/.. + c = 0 (A E ({;) '1
• tU~m~n5mru t.}+b'A+c = obtU~m~~tt:lHHtUJrn y"+by'+cy = Offits'i:lls

'Uhl 2 r:hGSSrl61tdthm 'U'i:llS'Uhl~'Ur:hGSSrl£1 'U'i:llS'Uhl 2 mdssfints '1
"'\.!) 1J tt r;; "1.!1. " 1 1J "'.!l. "\,!) lJ 16V

2.2. 'lfitm:uuurrrutJmratt4l~iruJnnihst'ffnhnti9 2 y"+bl+cy = o

n. nrn!ittHurutJmuJm nhnsu runrm fi s sfHnt.t~m
.; IJ 'U q;
1/f ~ qf II lcJ
!JtnVJUl/1: t~'i:llShl'i§fil~~tdHHhlJ05 y"+2y'-8y = 0 (E) '1
2
" hl~fll~ (E) 'i:llShl~fll~hlfflru 'A +2A-8 = 0

ttilru il' = 1-(-8) = 9 &S'Hhl~fmhlt=nru'i:llS~hl 2 r:hG~Srl61&dJh~~ -4

Sti 2 '1 hl~fll~ (E) h!lut'UHhl~r:h : (y' +4y)' -2(y' +4y) = 0

mil Z = y' +4y t~QIS : Z' -2Z = 0

Z' = 2Z 'U dZ = 2Z
"'- dx
dZ = 2dx
z
lniZI = 2x + c

= e2x+c ~:;:: z 2x ( ...... c
lzl "' I '11 = C J C b W rn C! = ±e )
2
ttilru Z = y'+4y &S'lH~QIS y'+4y = c e x
1

t~n1HLhllruhl~fil2 y' + 4y = o ~mq'U&'L"e'U~rn8~s trH
IJ
y' + 4y = 0 t~QIS dy = -4y
dx

dy = -4dx sl §1 In IYI = - 4x + c
y u
-4x ( " c
y = Cze ttJ 05 Cz = ±e )

.. " 0
r:gmL"e'UL"ernts~sr:n~ c 2 .:
IJ
115