Page 108 - Math Grade 12 (Advance)

PROEUS DARA

3. ~m.m :tMUJfUtrfili y' + ay = p(x) mtfifitrtttmnrruG88tta
lf lf
cr ~ e» u , e1 .....
2fTIU'JUU1: tR''i:flSti515fn~~ttHbi:ti5Jlli y'+2y = 3e--'"' (E) '1

1
1
fl. H'iGt~tl5!H9ils tU~fn~ )' + 2y = 0 (E ) '1
"' u
~- ffi,'jHS~'i5B f Rrulshtflru f(x) = e- xg(x) '1 R'MSl f'(x) dlHSR''i§~ns
2
I I
1
g(x) Sb g (x) '1 R'MSl g (X) ttl f(x) dlutiruls (E) '1
1
R'. 9lFIJH1 g(x) JG f(x) t~15j2J f(x) dlutirulstU~fn~ (E) '1
orfJw :
fill
""
"" "
1
n. ~ nut'i5liHS tU'i5 m~ Y + 2y = o (E')
"'
d)'
- = -2y il2J dy = -2dx
dx y
lnjyj = -2x+c
y = ±e 2x+c

-2x
y = Ae
1
2. R'MSl f'(x) Sb g (x)
-2x
f(x) = e g(x)
, -2x -2x 1
f (x) = - 2e g(x) + e g (x)

1 -3x
f (x) + 2f(x) = 3e
-2x -2 r , -2x -3 r
-2e g(x) + e · g (x) + 2e g(x) = 3e ·

e -2x '( ) J -3x
g x = e
3e-Jx -x
1
g (x) = --=2:; = 3e '1
e
1
R'. ttflru g (X) = 3e-x tSlg g(x) = J 3e-xdx = -3e-x + c
1
ttflru f(x) dlm~ruls (E) mrurun g (x) = 3e-x tSlg
G\J
-2x
f(x) = e g(x)

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