Question

CALCULUS: 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

-I am thinking A, but I would like someone to please double check me. Please no wrong/fake answers. Thanks in advance & have a good one!

Answer 1

A. Hyperbolas

Explanation:

Answer 2

This equation is separable; you have

x dx - y dy = 0

x dx = y dy

Integrate both sides to get

1/2 x ² + C = 1/2 y ²

x ² + C = y ²

or

x ² - y ² = C

and this is indeed the equation of a hyperbola.