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CBSE Class 12-science Answered

If x = a cos thita + b sin thita and y = a sin thita – b cos thita, show that y2d2y/dx2 – x dy/dx + y = 0 explain in great detail
Asked by haroonrashidgkp | 25 Aug, 2018, 07:15: PM
answered-by-expert Expert Answer
begin mathsize 16px style straight x equals acosθ plus bsinθ
straight y equals asinθ minus bcosθ
straight x squared plus straight y squared equals open parentheses acosθ plus bsinθ close parentheses squared plus open parentheses asinθ minus bcosθ close parentheses squared
straight x squared plus straight y squared equals straight a squared cos squared straight theta plus 2 absinθcosθ plus straight b squared sin squared straight theta plus straight a squared cos squared straight theta minus 2 absinθcosθ plus straight b squared cos squared straight theta
straight x squared plus straight y squared equals straight a squared cos squared straight theta plus straight a squared cos squared straight theta plus straight b squared sin squared straight theta plus straight b squared cos squared straight theta
straight x squared plus straight y squared equals straight a squared plus straight b squared
2 straight x plus 2 straight y dy over dx equals 0
straight x plus straight y dy over dx equals 0
rightwards double arrow dy over dx equals fraction numerator negative straight x over denominator straight y end fraction
rightwards double arrow fraction numerator straight d squared straight y over denominator dx squared end fraction equals negative fraction numerator straight y minus straight x dy over dx over denominator straight y squared end fraction
rightwards double arrow straight y squared fraction numerator straight d squared straight y over denominator dx squared end fraction equals negative straight y plus straight x dy over dx
rightwards double arrow straight y squared fraction numerator straight d squared straight y over denominator dx squared end fraction minus straight x dy over dx plus straight y equals 0



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Differentiate space straight y equals square root of fraction numerator straight x squared plus 2 over denominator straight x squared plus 3 end fraction end root 
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