Antidifferentiantion

Question

if dy/dx = -x/y, and (-3,4) solves the differential equation, then write the original equation.

Answer 1

y dy = - x dx

y²/2 = x²/2 + C

9/2 + 16/2 = C => C= 25/2

x² + y² = 25

Note: This is the equation of a circle with radius 5 centered at the origin.