Question

The differential equation `y ("d"y)/("d"x) + "c"` represents: ______.

विकल्प

• Family of hyperbolas

• Family of parabolas

• Family of ellipses

• Family of circles

Answer 1

The differential equation `y ("d"y)/("d"x) + "c"` represents: Family of circles.

Explanation:

Given differential equation is `y ("d"y)/("d"x) + x` = c

⇒ `y ("d"y)/("d"x)` = c – x

⇒ ydy = (c – x)dx

∴ Integrating both sides, we get

`int y  "d"y = int ("c" - x)  "d"x`

⇒ `y^2/2 = "c"x - x^2/2 + "k"`

⇒ `x^2/2 + y^2/2 - "c"x` = k

⇒ x² + y² – 2cx = 2k which is a family of circles.