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=x^{3             ..........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

---

Please feel free to post as many doubts on our discussion forum as you can.
 If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly.
 We are all IITians and here to help you in your IIT JEE  & AIEEE preparation.

 All the best.
 
Regards,
Askiitians Experts
Badiuddin