question_answer

The differential equation representing the family of curves\[{{y}^{2}}=2c(x+\sqrt{c}),\]where\[c>0,\]is a parameter, is of order and degree as follows       AIEEE  Solved  Paper-2005

A) order 2, degree 2

B) order 1, degree 3

C) order 1, degree 1

D) order 1, degree 2

Correct Answer: B

Solution :

The differential equation of a family of curves of n parameters is a differential equation of n order. Equation of family of curves is \[{{y}^{2}}=2\,c\,(x+\sqrt{c})\]                  ?(i) On differentiating Eq. (i) w.r.t. x, then           On putting the value of c in Eq. (i), we get Hence, the degree and order of above equation are 3 and 1, respectively.