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form the diff. eq. of the family of curves represented by,
c(y+c)2=x3;where c is any arbitrary constant.
Dear upendra
c(y+c)2=x3 ..........1
differentiate w.r.t x
2c(y+c) dy/dx =3x2
from euation 1 c(y+c) = x3/(y+c)
put it
2 x3/(y+c) dy/dx =3x2
2x/3 dy/dx =y+ c
put value of c to equation 1
(2x/3 dy/dx -y)(2x/3 dy/dx)2 =x3
(2x/3 dy/dx)3 -y(2x/3 dy/dx)2 =x3
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