## Differential Equations and Linear Algebra (4th Edition)

Differentiate the equation in respect to $x$. $$x^2+y^2=c$$ $$2x+2y \times y'=0$$ Solve for $y'$. $$y \times y'=-x$$ $$y'=-\frac{x}{y}$$ This expression matches the given differential equation $y'=-x/y$ exactly, therefore, the equation is a solution.