Question

find an equation that gives y as an implicit function of x. Then draw the continuous curve that satisfies this differential equation and passes through the point (2, 0).

$\frac{dy}{dx}=\frac{-x}{y}$

Short answer

$y^2=-x^2$

Step-by-step solution

Step 1. Given information

$\frac{dy}{dx}=\frac{-x}{y}$

Step 2. Rearrange and integrate

$ydy=-xdx$

$\int ydy=-\int xdx$

$\frac{y^2}{2}=-\frac{x^2}{2}$

$y^2=-x^2$