CBSE Class 12-science Answered

if y=[x+rt(x2+1)]^m, show that (x2+1)y2+xy1-m2y=0

Asked by lekhakarthikeyan | 05 Dec, 2018, 09:47: PM

Expert Answer

I assume the question is if

begin mathsize 12px style y space equals space open square brackets x plus square root of x squared plus 1 end root close square brackets to the power of m end style

, show that (x² + 1 )y₂ + xy₁ - m²y = 0

where

begin mathsize 12px style y subscript 1 space equals space fraction numerator d y over denominator d x end fraction space space space a n d space space y subscript 2 space equals space fraction numerator d squared y over denominator d x squared end fraction end style

begin mathsize 12px style y space equals space open square brackets x plus square root of x squared plus 1 end root close square brackets to the power of m space.................... left parenthesis 1 right parenthesis L e t space u s space d i f f e r e n t i a t e space e q n. left parenthesis 1 right parenthesis comma space fraction numerator d y over denominator d x end fraction equals y subscript 1 space equals space m space open square brackets x plus square root of x squared plus 1 end root close square brackets to the power of m minus 1 end exponent space space cross times open square brackets 1 space plus space fraction numerator 2 x over denominator 2 square root of x squared plus 1 end root end fraction close square brackets y subscript 1 space equals space m space open square brackets x plus square root of x squared plus 1 end root close square brackets to the power of m minus 1 end exponent space space cross times open square brackets fraction numerator x plus square root of x squared plus 1 end root over denominator square root of x squared plus 1 end root end fraction close square brackets y subscript 1 space space equals space fraction numerator m space open square brackets x plus square root of x squared plus 1 end root close square brackets to the power of m over denominator open parentheses square root of x squared plus 1 end root space close parentheses end fraction space space............ left parenthesis 2 right parenthesis A b o v e space e q n. left parenthesis 2 right parenthesis space c a n space b e space w r i t t e n space a s comma space space space space open parentheses space square root of x squared plus 1 end root space close parentheses space y subscript 1 space equals space m cross times y space............ left parenthesis 3 right parenthesis I f space w e space d i f f e r e n t i a t e space a b o v e space e q u a t i o n comma space w e space g e t space open parentheses space square root of x squared plus 1 end root space close parentheses space y subscript 2 space plus space fraction numerator x over denominator square root of x squared plus 1 end root end fraction space y subscript 1 space equals space m cross times y subscript 1 space............ left parenthesis 4 right parenthesis I n space e q n. left parenthesis 4 right parenthesis comma space a t space R H S comma space w e space s u b s t i t u t e space e q n. left parenthesis 3 right parenthesis space f o r space y subscript 1 space t o space g e t space open parentheses space square root of x squared plus 1 end root space close parentheses space y subscript 2 space plus space fraction numerator x over denominator square root of x squared plus 1 end root end fraction space y subscript 1 space equals space m cross times fraction numerator m cross times y over denominator square root of x squared plus 1 end root end fraction space........... left parenthesis 5 right parenthesis M u l t i p l y i n g space a b o v e space e q u a t i o n space b y space square root of x squared plus 1 end root space o n space b o t h space s i d e space a n d space r e a r r a n g i n g space t e r m s space w e space g e t open parentheses x squared plus 1 close parentheses space y subscript 2 space plus space x space y subscript 1 space minus space m squared y space equals space 0 end style

Answered by Thiyagarajan K | 06 Dec, 2018, 05:22: AM

CBSE Class 12-science Answered

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CBSE Class 12-science Answered

Application Videos

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Concept Videos

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