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. order 2, degree 4
C. order 1, degree 5
D. order 5, degree 1

Answer

C

Explanation

`y^(2)=2c(x+c^(2//3))`
`implies2y(dy)/(dx)=2cimpliesc=y(dy)/(dx)`
`:.y^(2)=2y(dy)/(dx)(x+(y(dy)/(dx))^(2//3))`
`implies((y)/(2(dy)/(dx))-x)=(y(dy)/(dx))^(2//3)`
`implies(y-2x(dy)/(dx))^(3)=(2(dy)/(dx))^(3)(y(dy)/(dx))^(2)`
`implies(y-2x(dy)/(dx))^(3)=8y^(2)((dy)/(dx))^(5)`
Here, order = 1, degree = 5