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  • Find the diffrential equation whose solution represents the family : c(y+c)^2=x^3

Find the diffrential equation whose solution represents the family : c(y+c)^2=x^3

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Solution:      

          c(y+c)^2=x^3      .........(1)

     Diffrentiating , we get 2c(y+c)fracmathrmd ymathrmd x=3x^2

    Writing the value of c from (1) we have,

   Rightarrow    (2x^3/y+c)fracmathrmd ymathrmd x=3x^2

 I.e     (2x/y+c)fracmathrmd ymathrmd x=3Rightarrow (2x/3)fracmathrmd ymathrmd x=y+c

 Hence      c=(2x/3)fracmathrmd ymathrmd x-y

   Substituting value of c in equation  (1) , we get     [(2x/3)fracmathrmd ymathrmd x-y][(2x/3)fracmathrmd ymathrmd x]^2=x^3

 Which is the requried diffrential equation.

Posted by

Deependra Verma

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