If y = acos(logx) + bsin(log x), prove that x2y2  + xy1 + y = 0

Explain in great detail

 

Asked by haroonrashidgkp | 24th Aug, 2018, 11:11: PM

Expert Answer:

y = acos(log x) + bsin(log x)
begin mathsize 16px style dy over dx equals fraction numerator begin display style negative asin left parenthesis logx right parenthesis end style over denominator straight x end fraction plus fraction numerator bsin left parenthesis logx right parenthesis over denominator straight x end fraction
straight x fraction numerator begin display style dy end style over denominator begin display style dx end style end fraction equals negative asin left parenthesis logx right parenthesis plus bsin left parenthesis logx right parenthesis
straight x fraction numerator begin display style straight d squared straight y end style over denominator begin display style dx squared end style end fraction plus fraction numerator begin display style dy end style over denominator begin display style dx end style end fraction equals fraction numerator begin display style negative acos left parenthesis logx right parenthesis end style over denominator straight x end fraction minus fraction numerator bsin left parenthesis logx right parenthesis over denominator straight x end fraction
straight x squared fraction numerator begin display style straight d squared straight y end style over denominator begin display style dx squared end style end fraction plus straight x fraction numerator begin display style dy end style over denominator begin display style dx end style end fraction equals negative acos left parenthesis logx right parenthesis minus bsin left parenthesis logx right parenthesis
straight x squared fraction numerator begin display style straight d squared straight y end style over denominator begin display style dx squared end style end fraction plus straight x fraction numerator begin display style dy end style over denominator begin display style dx end style end fraction equals negative straight y
straight x squared fraction numerator begin display style straight d squared straight y end style over denominator begin display style dx squared end style end fraction plus straight x fraction numerator begin display style dy end style over denominator begin display style dx end style end fraction plus straight y equals 0 end style

Answered by Sneha shidid | 27th Aug, 2018, 10:21: AM