Page 109 - Math Grade 12 (Advance)

PROEUS DARA

-2t
f(x) = e · g(x) '1
e» .......4~ C» 1 c:P 2r
tH'i:Hi59tl:fJ!:!Hu1:Hfl~ y +2y = 0 l:i f(x) = Ae-. '1
"" u

1aufl,11f!l,11I21GUStrJt : tfh~jn:iHLMliHo~m~ yl + ay = p(x) (E) , p(x) * o
JIJ
u:rut?ilf~ :
u
- H'itH~ru~t9it!:Ht5~fil~ y' +ay = 0 ?i y = Ae-ax

t:» ' 0 0 r:!
- fifHH'i:Hi5 y = Ae-a., d!Ht5132Std~ A t!:llti5H2?1'l52 A(x)
.. GIJ lJ lJ 1
1
"' ax "'._, 1 ..S ._, "' ,
- tly = A(x)e- 17lm~ny 1 mrun y Swy wShlfiwhl'l5filly +ay = p(x)
"" lJ lJ ..
1
y = A(x)e-ax

1
(E) A (x)e-ax_aA(x)e-ax+aA(x)e-ax = p(x)
A (x)e-ax = p(x)
1

A'(x) = eax p(x)

0
e
A(x) = J xp(x)dx + c
~msg y = e-ax[J eaxp(x)dx + c]

., -ax.,.._, -axf ax
ti:lru Yc = ce · Sw Yp = e · e · p(x)dx '1

1
n. )' + y = 2ex
2 2
1
2. )' + )' = X
l:i. y' + y = cosx + sinx '1

104