Chapter 6 - Differential Equations - 6.3 Exercises - Page 421: 32

$${x^2} + {y^2} = 2C$$

$$\eqalign{ & \frac{{dy}}{{dx}} = - \frac{x}{y} \cr & {\text{Separate the variables}} \cr & ydy = - xdx \cr & {\text{Integrate both sides}} \cr & \int {ydy} = - \int {xdx} \cr & \frac{1}{2}{y^2} = - \frac{1}{2}{x^2} + C \cr & {x^2} + {y^2} = 2C \cr & {\text{Graph}} \cr} $$