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Vector Algebra

Question
CBSEENMA12032942

Form the differential equation corresponding to y2 = a (b – x) (b + x) by eliminating a and b.

Solution
The given equation is
              straight y squared space equals straight a space left parenthesis straight b minus straight x right parenthesis space left parenthesis straight b plus straight x right parenthesis space space or space space straight y squared space equals straight a space left parenthesis straight b squared minus straight x squared right parenthesis                  ...(1)
therefore space space space space space 2 straight y dy over dx space equals space straight a left parenthesis negative 2 straight x right parenthesis space or space straight y dy over dx space equals space minus ax                                 ...(2)
Again straight y fraction numerator straight d squared straight y over denominator dx squared end fraction plus dy over dx. dy over dx space equals space minus straight a                                                 ...(3)
 Eliminating a from (2) and (3), we get,
                           straight y dy over dx space equals space xy fraction numerator straight d squared straight y over denominator dx squared end fraction plus straight x open parentheses dy over dx close parentheses squared space space or space space straight x space straight y fraction numerator straight d squared straight y over denominator dx squared end fraction plus straight x open parentheses dy over dx close parentheses squared minus straight y dy over dx equals 0
which is the required differential equation.