Question

Form a differential equation of the family of the curves y² = 4ax.

Answer 1

Given: y² = 4ax

Differentiating both sides w.r.t. x, we get

`2y dy/dx = 4a`

⇒ `2y dy/dx = y^2/x`   ...`[∵ 4a = y^2/x]`

⇒ `2 dy/dx = y/x`

⇒ `2x dy/dx - y = 0`,

which is the required differential equation.