Page 123 - Math Grade 12 (Advance)

PROEUS DARA

t:Jf Ql C!) II l eJ
1
Sfl1fJJWJ1 : &r::iHLM11Hl5'13 fil~ ~ t~ ~iH MJ ru y" + 4y + 4y = 0 (E)
2
tuUm: nJ{§fil~f'15mnHsnJ{§fil~ (E) ~ A. +4A+4 = o

1
(E) ffitihlHhlHh (y + 2y)' + 2(y' + 2y) = 0 (i)
mb z = y' +2y

(i) : Z' + 2Z = 0

dZ o~ dZ
- = -2Z Sl~~ - = -2dx
dx u Z
lniZI = -2x+c

Z = Ae-Zx (A=±/)

A -2x
ll
'"""'"'"' 1 y+ 2 y= e (. ')
... 1'-11"'
... ., 0
tgtHL't3'i5L't3bliti~Std~ c 1 :
lJ
-2x 1 1 -2x -2x
y = c (x ) e , y = c (x)e 2c (x)e
1 1 1

1 -2x -2x
c (x)e = Ae
1
0
c' ( x) = A sl 2J c ( x) = Ax + B cs mcrsstda)
1
1
IJ
t:Jmsg y = (Ax+B)e-zx = Axe- x +Be-zx '1 £?1tnStit{§rugcsrf&snJ{§fila'2t~HHM~ru
2
U N U ~
2
y"+4y'+4y = 0 ~ y = Axe- x+Be-zx tt:Jru A sb B mf3sstdH1..ffi't3115RtnS '1
IJ IJ
thft£11: t-i5hl{§fmfi5mrn A +bA+c = 0 ~shl{§fm2t~~t1tMJbli
2
y"+by'+cy = O'i:f12'i5M~'i5thQSStln '?i A. = A. =a £Slg£?1tn2crt{§rugt94
2
1
"' l IJ 6V u

0
W'i.ITI tff!iJ : n::tu L nn ru.M'\3 nu c E) : y" + 2y' + y = 0 ffi't3blin2Mt~'t3 y(ln2) = I
' 0
eJ
9 ~ 2
sb y'(ln2) = - 1 '1
"'
2
118