Page 116 - Math Grade 12 (Advance)

PROEUS DARA

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6. t?lffi2hl~fil~~tti~tlf'hlJbl5 (E) : y'+2y = x '1

n. RMS'intnm 8 ms~ t'in'9 2 ttl rnr:hm~run thlhl~s (E) '1
t G w
cl C) Q)l Q)l ";) Qf t:::J} II I C)
~. mb h r:hH2?11:52ttlbl5 h(x) = f(x) g(x) '1 ttl h r:htH't:5li5t2hl't:5fil~~Hjj~tithl'ibl5
t "' i:J

1=1 tt:tuunnruhl~fil~ y' + 2y = o HHfl m~nH2?11:5S f ttl rnr:hm~ru~:H9'i~s (E) '1
Ll '-' t GVU
7. t?lffi2hl~fil~~tti~tlfhlJbl5 (E): y'-2y= +-:-2x
1
n. t1flgLnnruhl~fil~~tti'~tlfhlJb15 y' -2y = o f!:1rnt~b~S'i y(O) = 1 '1

d ~ CJ 'x d~
~. mb f r:hH2?11:52ffi2ttlH~ IR ttlbl5 f(x) = e~ g(x) '1 ?lrulSl f(x) r:hHS?11:521:2
t 1
g(x) sb g'(x) '1
-2x
2
1=1. tiblmrtau f r:hm~ru~s (E) rngLmfs; g'(x) = - e '1
2
U1....., "' t l+e-x
"' "" ,
ill. tnm~nntsn't:5 g(x) w f(x) t!:1rn f r:htH1:5li5t2 (E) '1
~ u· w w
8. tcngLnnruhl~fil~~ttiitlfhlJrn :
_ dy 3x o. dy + Y = __ _
I
n. dx- y = e o - ?1. y' + y = 1 ill. y' + y = sinx '1
dx 1 + ix
9. ten gLnnru hl~fil~~ tti~tl fhlJbl5ffl't:5 rnQ~ o.g tt11:5

n. y'- y = 1 , y(O) = 1 ~.y' + 2y = 1 , y(O) = 0 '1

3x X dy
n. ~~ = sin5x ~. dx+ e dy = 0 ?1. e dx = 2x
dy 2
ill. (x + l )~~ = x + 6 b. dx- y = -9 , y(O) = 3 '1

tc:p ~ ot::::l Oc::t. eJ 0~
11. t?11:rln9n 100 bl5'itinbwb1:5rusbH'Urn IOkg ttlrn'in~Hlllrunbwbtmg '1 rnnruH'Urn
lict t Ll li .. t ~-~·
t u t
C) 0 t::::l. c::p ~ Ql
1:5ruttlrnmsH'Ubl5 o.3kg nb9n't:5li5rn'in'iSi~tibmrnnbwbtsgt1flruH;m 8 bl51nnb1:5ru
Ll ct Ll lili U1U ct t li ljc; 1.1
t u u t 1
S1'9 '1 rnnruu'i't:5Hsinbwb1n1t?ln~ W'UbHumt1:rlli5H'iffl 8 ru'innb1:5li5S1'9 '1
~-~· t_; .. t li u IJ U1 ....., li ljc; Ll
t t u u t
n. 1nrnn~Mta't:5~srhrung tS1:5'1?1MS1ti1mM~lirn Q(t) tsinbwb
B S eJ ctt
t
~. ?1MS1ti1mM~lirn Q(t) ~b~b tsi~M: t ~tLfilrutnrnti~~ms 25 m9 '1
t u

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