The differential equation representing the family of curves `y^2=2c(x+sqrt(c)),` where `c` is a positive parameter, is of (a) order 1 (b) order 2 (c) degree 3 (d) degree 4

Options

A. order 1 and degree 3
B. order 2 and degree 3
C. order 1 degree 2
D. none of these

Answer

A

Explanation

We have,
`y^(2)=2c(x+sqrtc)" …(i)"`
`rArr" "2yy_(1)=2c`
`rArr" "yy_(1)=c" …(ii)"`
Eliminating c from (i) and (ii), we get
`y^(2)=2yy_(1)(x+sqrt(yy_(1)))`
`rArr" "y-2xy_(1)=(sqrtyy_(1))^(3//2)rArr (y-2xy_(1))^(2)=(yy_(1))^(3)`
Clearly, it is a differential equation of order one and degree 3.