Question

The solution of the differential equation xdx + ydy = 0 represents a family of ______.

Options

• straight line

• parabolas

• circles

• ellipses

Answer 1

The solution of the differential equation xdx + ydy = 0 represents a family of circles.

Explanation:

Now, xdx + ydy = 0

xdx = –ydy

Integrating both sides:

∫ xdx = –∫ ydy

x² + C₁ = –y² + C₂

x² + y² = C₂ – C₁

x² + y² = k

This is the equation of a circle.