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The differential equation for the family of curves y=c sin x

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Solution:         y=csin x           ..........(1)

              herefore       fracmathrmd ymathrmd x=ccos x          ..........(2)

             From   (2)

             Rightarrow      (fracmathrmd ymathrmd x)^2=c^2cos^2x      .........(3)

           Putting      c=fracysin xRightarrow (fracmathrmd ymathrmd x)^2=y^2cot^2x

          Eliminating c  from (1) and (2) ,  fracmathrmd ymathrmd x=ycot x

       Squaring and adding (1) and (2)      y^2+(fracmathrmd ymathrmd x)^2=c^2

     Putting the value of c from (3)  , y^2+(fracmathrmd ymathrmd x)^2=(fracmathrmd ymathrmd xsec x)^2

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Deependra Verma

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