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 t…

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asked Apr 17, 2022 118k views

2 Answers

Cristianoms · Answer 1 · 2022-04-24T04:16:30+0000

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.