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CBSE Class 12-science Answered

If y = sin(log x), prove that x2d2y/dx2 + xdy/dx  + y = 0   Explain in great detail  
Asked by haroonrashidgkp | 25 Aug, 2018, 07:06: PM
answered-by-expert Expert Answer
begin mathsize 16px style To space prove colon straight x squared fraction numerator straight d squared straight y over denominator dx squared end fraction space plus space straight x space dy over dx space plus space straight y space equals space 0 straight y space equals space sin left parenthesis logx right parenthesis dy over dx equals space straight d over dx sin left parenthesis logx right parenthesis space space space space space space equals space cos left parenthesis logx right parenthesis. straight d over dx logx space space space space space space space space equals space cos left parenthesis logx right parenthesis.1 over straight x space space space space equals space fraction numerator cos left parenthesis logx right parenthesis over denominator straight x end fraction space space space.... left parenthesis 1 right parenthesis fraction numerator straight d squared straight y over denominator dx squared end fraction space equals straight d over dx open parentheses dy over dx close parentheses space space space space space space space equals straight d over dx space fraction numerator cos left parenthesis logx right parenthesis over denominator straight x end fraction space space space space space space equals space fraction numerator straight x begin display style straight d over dx end style open square brackets cos left parenthesis logx right parenthesis close square brackets minus space cos left parenthesis logx right parenthesis straight d over dx straight x over denominator straight x squared end fraction space space space space space space equals fraction numerator straight x open square brackets negative sin left parenthesis logx right parenthesis. space begin display style 1 over straight x end style close square brackets minus cos left parenthesis logx right parenthesis.1 space over denominator straight x squared end fraction space space space space space space equals space fraction numerator negative sin left parenthesis logx right parenthesis over denominator straight x squared end fraction space minus space fraction numerator cos left parenthesis logx right parenthesis over denominator straight x squared end fraction space space space space.... left parenthesis 2 right parenthesis straight L. straight H. straight S space equals straight x squared fraction numerator straight d squared straight y over denominator dx squared end fraction space plus space straight x space dy over dx space plus space straight y space space space space space space space space space space space equals space straight x squared open square brackets fraction numerator negative sin left parenthesis logx right parenthesis over denominator straight x squared end fraction space minus space fraction numerator cos left parenthesis logx right parenthesis over denominator straight x squared end fraction close square brackets space plus space straight x open square brackets fraction numerator cos left parenthesis logx right parenthesis over denominator straight x end fraction close square brackets space space plus space sin left parenthesis logx right parenthesis space space space space space space space space space equals 0 space space space space space space space space space equals space straight R. straight H. straight S Hence comma space proved. end style
Answered by Yasmeen Khan | 27 Aug, 2018, 02:33: PM

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