Page 124 - Math Grade 12 (Advance)

PROEUS DARA

GtfJw :
fll
~ ~ 0 I 2 ~
• hl'i.:H'il~ y"+2y'+y = 0 'HlShl13ffl~hlffH15 A +2A+ 1 =0 'HlS'lihl~'i.H1
'-' I
AI = A2 = -1

~msg 1:H~t159t91~Shl~ffl~ (E) ~ y = Axe-x+Be-x ttH15 A Sb B
u 6V u
0 ~
dluSSt0Hl.Jll13t15nQlS '1
!J !J

B -~
y(ln2) = - 1 - = AI 2 -~ 2 + e 2
I
n e
2 2
~ = ~Aln2 + ~B
2 2 2
A1n2+B = 1 (i)

. I
t r:tl ru y' (In 2) = - - - I _ A -In2 AI n 2 e -In2 B -ln2
-
e
-
e
-
2 2
- ~ = ~A - ~A In 2 - ~ B
2 2 2 2
-1 = A-Ain2-B (ii)
(i) Sb (ii) : { Aln2+B = I o§ {A= 0
A - A In 2 - B = -I S1 U B = I
~
"
""
1 "'
""
"'
[:lfHSg y = e-x dlut13t15rlthlhltS ft513ffl~ (E) ffl13blin2 C1.fHL:J13 y(ln2) = - Sb
U GV B lil 2
y'(ln2) = - ~ '1
2
1J1Rug: tr:tl gLhllru hl~ffl~ ~ tdiiH'hlJ rn 4y"- 4y' + y = o m-e rnQ2 n.g tt3-e
"'14 ,
y(O) = -3 2'1...1 y (0) = 2 '1

y"+by'+cy = o '1 tiblmmd5
U1 ._..,
er C» ~ '> c::t. C»
H~l:l-es y = y (x) + iJ2(x) dlm~rumtututs (E) tSlg y (x) sb y (x) dlm~rutmrn
1
1
2
ls (E) ~u9lm~nm~ru9tvlts (E) '1
!J ._.., 6V u

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