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form the diff. eq. of the family of curves represented by, c(y+c) 2 =x 3 ;where c is any arbitrary constant.

form the diff. eq. of the family of curves represented by,


c(y+c)2=x3;where c is any arbitrary constant.

Grade:12

1 Answers

Badiuddin askIITians.ismu Expert
147 Points
11 years ago

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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