Question

The differential equation representing the family of curves y² = `2c(x + sqrt(c))`, where c is a positive parameter, is of ______.

Options

• order 3

• order 2

• degree 3

• degree 4

Answer 1

The differential equation representing the family of curves y² = `2c(x + sqrt(c))`, where c is a positive parameter, is of degree 3.

Explanation:

2yy₁ = 2c

`\implies` c = yy₁

Eliminating c, we get, y² = `2yy_1 (x + sqrt(yy_1))`

or (y² – 2x yy₁)² = `4y^3y_1^3`

It involves only 1st order derivative, its degree is 3 as `y_1^3` is there.