Curves general solutions

Question

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

hyperbolas

circles

parabolas

Ellipses

Answer 1

x dx + y dy = 0

 

2x dx = -2y dy

 

x² = -y² + C

 

x² + y² = C

 

These are circles.