The general solution of the differential equation x dx + y dy = 0 is a family of curves. These curves are all

Question

The general solution of the differential equation x dx + y dy = 0 is a family of curves. These curves are all ?

A.) Hyperbolas

B.) Circles

C.) Parabolas

D.) Ellipses

Answer 1

xdx + ydy = 0

ydy = -xdx

Integrate both sides to get (1/2)y² = -(1/2)x² + C

So, x² + y² = C, which is a family of circles.