Page 129 - Math Grade 12 (Advance)

PROEUS DARA

y" +by'+ cy = p(x) , p(x) :t 0

- ftubH1tH~t15rltnHi.r@swt'Htus mb tftl t15 Yp tEl hl~fil~ y" +by'+ cy = p(x)
~ "" u u
fL:j m Yp 'l:f1El9L'ijti~uH~9 2 p(x)

- HiU£~ t159 tvi mb t ftl t15yc tEl hl~ filHli tEl tH ru ftltig 2 w!H'tu Ely"+ by'+ cy = 0
"" u u u

c:i>
Yp f!'i Y = Yc+Yp '1

II) tO Ql alof"'!!U~CJ 2
flJtmlff.'i/ : tf!'i'l:flEl t1j'ij f\l~ ~ t i-:1 ~w ~MJ ru y"- 2y'- 3y = 6x -X (E) '1

2. ~nut~t159t94 Yc tElhl~f\l~ y"-2y'-3y = 0 '1
"" u
f!'i. r~bg1~m y = Yc+ Yp r:hm~rugrvits (E) ~cr9lm~nm~rugr94ts (E) '1
&J ~ GV U 1J '-' 6V U
cu1Jw :
<Ill

tftlru Yp = ai + bx + c tf!'iOIS : y'P = 2ax + b , y"P = 2a
2
y"P-2y'p-3Yp = 2a-2(2ax+b)-3(ax +bx+c)
2 2
tf!'it(lS: 2a-4ax-2b-3ax -3bx-3c = 6x -x
2 2
-3ax -(4a+3b)x+2a-2b-3c = 6x -x

(-3a) = 6
4a + 3b = I
{
2a-2b- 3c =

10
"
"'
""'
2
l:lmsg y = 2x + 3x--- r:hcrmrumtututs (E) '1
U p 3 GV
C» .-4 ':) 1:::1 II J
2. ~n13t1§t159t::ntSM'ijf\l~ y -2y -3y = 0
"" u
~ Q 0 I
tu1§fil~ y"--2y'-3y = o 'l:f1Stu1§fil~tumm J....2 2A-3 = o &t~ru'l:flsutu 2
"'
tdJb ~~ 1. 1 = I , 1- 2 = 3
-x 3x
Yc = Ae +Be '1
124