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CBSE Class 12-science Answered

If y = {x + (x2 + 1)1/2}m then show that (x2 + 1)d2y/dx2 + x dy/dx – m2y = 0
Asked by haroonrashidgkp | 25 Aug, 2018, 07:13: PM
answered-by-expert Expert Answer
begin mathsize 16px style straight y equals open parentheses straight x plus square root of straight x squared plus 1 end root close parentheses to the power of straight m
dy over dx equals straight m open parentheses straight x plus square root of straight x squared plus 1 end root close parentheses to the power of straight m minus 1 end exponent cross times open parentheses 1 plus fraction numerator 1 over denominator 2 square root of straight x squared plus 1 end root end fraction cross times 2 straight x close parentheses
dy over dx equals straight m open parentheses straight x plus square root of straight x squared plus 1 end root close parentheses to the power of straight m minus 1 end exponent cross times open parentheses fraction numerator straight x plus square root of straight x squared plus 1 end root over denominator square root of straight x squared plus 1 end root end fraction close parentheses
dy over dx equals straight m open parentheses straight x plus square root of straight x squared plus 1 end root close parentheses to the power of straight m cross times fraction numerator 1 over denominator square root of straight x squared plus 1 end root end fraction
square root of straight x squared plus 1 end root dy over dx equals straight m open parentheses straight x plus square root of straight x squared plus 1 end root close parentheses to the power of straight m
open parentheses straight x squared plus 1 close parentheses open parentheses dy over dx close parentheses squared equals straight m squared straight y squared
open parentheses straight x squared plus 1 close parentheses 2 dy over dx fraction numerator straight d squared straight y over denominator dx squared end fraction plus open parentheses dy over dx close parentheses squared 2 straight x equals straight m squared 2 straight y dy over dx
open parentheses straight x squared plus 1 close parentheses fraction numerator straight d squared straight y over denominator dx squared end fraction plus open parentheses dy over dx close parentheses straight x equals straight m squared straight y
open parentheses straight x squared plus 1 close parentheses fraction numerator straight d squared straight y over denominator dx squared end fraction plus open parentheses dy over dx close parentheses straight x minus straight m squared straight y equals 0
end style
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