The differential equation representing the family of curves ` y^(2) = 2c (x +c^(2//3))` , where c is a positive parameter , is of

Options

A. order 3, degree 3
B. order2,degree4
C. order 1,degree 5
D. order 5,degree 1

Answer

c

Explanation

` y^(2) = 2c (x+c^(2//3))`
On differentiating both sides , we get op
` rArr 2y (dy)/(dx) = 2c rArr c = y (dy)/(dx)`
` :. y^(2) = 2y (dy)/(dx) [ x + (y (dy)/dx)^(2//3)]`
` rArr (y/(2(dy)/dx)-x) = (y (dy)/(dx))^(2//3)`
` rArr (y - 2x (dy)/(dx))^(3) = (2 (dy)/dx)^(3) (y (dy)/(dx))^(2)`
` rArr (y - 2x (dy)/(dx))^(3) = 8y^(2)(dy/dx)^(5)`
Here , order = 1, degree = 5