Page 128 - Math Grade 12 (Advance)

PROEUS DARA

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~fl1ff)Ul./1: tf:'l'i:flfHi51Hfl~~Hd~btfdJb15 y"-y = 2x (E) '1

n. miHHlf:113S <P fin..n~nt1ru <r(x) = -2x '1 ummmH2f:113S <P mm~ru&s (E)
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2. ~nHSti'eS g tL:J rut:htH'ef551H94 tS fd'efil~ y"- y = 0
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r:1. tdlbm~mHsr:;-es f = g+<r mm~ru&s (E) '1 &llminHsr:;-es f '1
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"" <p(x) t:htH13f55tS (E) tSH tf:'IOIS <p"(x) <p(x) = 2x
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tl:llru <p(x) = -2x tmg <p'(x) = -2 , <p"(x) = 0

<p"(x)-<p(x) = 0-(-2x) = 2x

[jfH28 <p(x) = -2x t:htH13f55tS
"" " (E) '1
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2. fd'efil~ y"- y = 0 'i:flS fd13fili fdfflru 'A - 1 = 0 , A- = -1 , A- = 1
1 2

f:'l. f = g + <P il2J f' = g' + <P' , f' = g" + <p"

f'(x)- f(x) = (g" + <p")(x)- (g + <p)(x) = g"(x)- g(x) + <p"(x)- <p(x)

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tw1ru g(x) J...J1tH~f55tS y y = 0 tmg g (x)-g(x) = 0
<p(x) t:hm~ruts (E) tmg <p"(x)-<p(x) = 2x
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i:ltHS8 f'(x)-f(x) = 2x mmr\:m f(x) t:htH~f55tS (E)
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f(x) = g(x) + <p(x) = Ae-x + Bex 2x

i:ltHS8 f(x) = Ae-x + Bex 2x t:htH~f559t94ts (E) '1
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" <p(x) = -2x t:h rlUHrl'i:flS91'e\:1 i:lt.mb9 2 ts fd~fili (E) '1 <p(x) tUTlmm~ru
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"g(x) t:htH'ef559tl:fi&Sfd13fil~ y"-y = 0
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" tH~f55~t94tSfd~fili (E) ~ f(x) = g(x)+<p(x) '1

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