Question

The differential equation representing the family of curves `y^2 = 2d(x + sqrtd)`, where d is a positive parameter, is of ______ 

पर्याय

• order 2

• degree 2

• degree 3

• degree 4

Answer 1

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

Explanation:

`y^2 = 2d(x + sqrtd)` ...........(i)

Differentiating w.r.t. x, we get

`2y dy/dx = 2d` .................(ii)

Substituting (ii) in (i), we get

`y^2 = 2y dy/dx(x + sqrt(y dy/dx))`

⇒ `y = 2x dy/dx + 2dy/dx . sqrt(y dy/dx)`

⇒ `(y - 2x dy/dx)^2 = 4y(dy/dx)^3`

This is a differential equation of order 1 and degree 3.